ZZZZ
FILE INFORMATION
FILENAME(S): ZZZZ
FILE TYPE(S): PRG
FILE SIZE: 35.9K
FIRST SEEN: 2025-11-30 16:59:42
APPEARS ON: 1 disk(s)
FILE HASH
ac594fb576cb3c56d28f89d8dec329f121c3f847d5f5a603b0d1bf51dffcec01
FOUND ON DISKS (1 DISKS)
| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| MATHS TUTOR 1 | ZZZZ | PRG | High Voltage Complete C64 Collection | 12 | 2 | DOWNLOAD FILE |
FILE CONTENT & ANALYSIS
> DETECTED: COMMODORE BASIC PROGRAM (LOAD ADDRESS $0801)
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00003880: 53 49 4D 50 4C 49 46 59 20 35 58 2D 34 28 32 58 |SIMPLIFY 5X-4(2X|
00003890: 2D 33 29 22 3A 99 00 D0 40 CE 2C 99 22 20 9F 53 |-3)":...@.,." .S|
000038A0: 4F 4C 55 54 49 4F 4E 3A 9A 20 52 45 4D 4F 56 45 |OLUTION:. REMOVE|
000038B0: 20 54 48 45 20 28 A0 29 20 41 28 96 42 9A 2B 1E | THE (.) A(.B.+.|
000038C0: 43 9A 29 3D 41 96 42 9A 2B 41 1E 43 9A 22 3A 99 |C.)=A.B.+A.C.":.|
000038D0: 00 09 41 D8 2C 99 22 20 53 4F 20 2D 34 28 96 32 |..A.,." SO -4(.2|
000038E0: 58 9A 2D 1E 33 9A 29 20 3D 20 2D 34 28 96 32 58 |X.-.3.) = -4(.2X|
000038F0: 9A 29 2D 28 2D 34 29 28 1E 33 9A 29 20 3D 20 2D |.)-(-4)(.3.) = -|
00003900: 38 58 2B 31 32 2E 22 3A 99 00 3A 41 DD 2C 99 22 |8X+12.":..:A.,."|
00003910: 20 20 35 58 2D 34 28 32 58 2D 33 29 2C 20 54 48 | 5X-4(2X-3), TH|
00003920: 45 4E 2C 20 45 51 55 41 4C 53 20 20 20 20 35 58 |EN, EQUALS 5X|
00003930: 2D 38 58 2B 31 32 2E 22 3A 99 00 71 41 E2 2C 99 |-8X+12.":..qA.,.|
00003940: 22 20 43 4F 4C 4C 45 43 54 20 4C 49 4B 45 20 54 |" COLLECT LIKE T|
00003950: 45 52 4D 53 2E 20 35 96 58 9A 2D 38 96 58 9A 2B |ERMS. 5.X.-8.X.+|
00003960: 31 32 20 3D 20 2D 33 96 58 9A 2B 31 32 2E 22 3A |12 = -3.X.+12.":|
00003970: 99 00 A1 41 EC 2C 99 22 20 53 49 4E 43 45 20 41 |...A.,." SINCE A|
00003980: 2B 42 3D 42 2B 41 20 2D 33 2B 31 32 58 20 43 4F |+B=B+A -3+12X CO|
00003990: 55 4C 44 20 42 45 20 57 52 49 54 54 45 4E 22 3A |ULD BE WRITTEN":|
000039A0: 99 00 CB 41 F6 2C 99 22 20 41 53 20 31 32 58 2D |...A.,." AS 12X-|
000039B0: 33 2E 20 4F 4B 20 22 41 31 24 22 20 4E 4F 57 20 |3. OK "A1$" NOW |
000039C0: 59 4F 55 20 54 52 59 3A 22 3A 99 00 00 42 00 2D |YOU TRY:":...B.-|
000039D0: 97 31 39 38 2C 30 3A 85 20 22 20 53 49 4D 50 4C |.198,0:. " SIMPL|
000039E0: 49 46 59 20 32 28 58 2B 33 29 2B 33 28 58 2D 32 |IFY 2(X+3)+3(X-2|
000039F0: 29 20 12 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 |) ...";B1$:.".."|
00003A00: 00 14 42 0A 2D 8B 42 31 24 B2 22 35 58 22 89 31 |..B.-.B1$."5X".1|
00003A10: 31 35 37 30 00 43 42 14 2D 99 22 20 4E 4F 2C 20 |1570.CB.-." NO, |
00003A20: 12 35 58 92 20 49 53 20 43 4F 52 52 45 43 54 2E |.5X. IS CORRECT.|
00003A30: 20 32 28 58 2B 33 29 2B 33 28 58 2D 32 29 20 3D | 2(X+3)+3(X-2) =|
00003A40: 22 3A 99 00 74 42 1E 2D 99 22 20 32 58 2B 36 20 |":..tB.-." 2X+6 |
00003A50: 2B 20 33 58 2D 36 20 3D 20 32 58 2B 33 58 2B 36 |+ 3X-6 = 2X+3X+6|
00003A60: 2D 36 20 3D 20 35 58 2B 30 20 3D 20 12 35 58 92 |-6 = 5X+0 = .5X.|
00003A70: 2E 22 3A 99 00 A1 42 28 2D 99 22 20 52 45 4D 45 |.":...B(-." REME|
00003A80: 4D 42 45 52 20 22 41 31 24 22 2C 20 54 4F 20 53 |MBER "A1$", TO S|
00003A90: 49 4D 50 4C 49 46 59 22 3A 99 3A 89 31 31 34 30 |IMPLIFY":.:.1140|
00003AA0: 30 00 AB 42 32 2D 8D 39 30 30 30 00 DC 42 3C 2D |0..B2-.9000..B<-|
00003AB0: 99 22 20 54 48 45 20 43 4F 4D 4D 55 54 41 54 49 |." THE COMMUTATI|
00003AC0: 56 45 20 4C 41 57 20 48 4F 4C 44 53 20 46 30 52 |VE LAW HOLDS F0R|
00003AD0: 20 41 4E 59 20 4E 55 4D 2D 22 3A 99 00 0D 43 46 | ANY NUM-":...CF|
00003AE0: 2D 99 22 20 42 45 52 20 4F 46 20 54 45 52 4D 53 |-." BER OF TERMS|
00003AF0: 2C 20 45 47 20 41 28 42 2B 43 2B 44 29 3D 41 42 |, EG A(B+C+D)=AB|
00003B00: 2B 41 43 2B 41 44 2C 20 53 4F 22 3A 99 00 3F 43 |+AC+AD, SO":..?C|
00003B10: 50 2D 99 22 20 32 28 58 91 32 11 2D 34 58 2B 33 |P-." 2(X.2.-4X+3|
00003B20: 29 20 3D 20 32 58 91 32 11 2D 38 58 2B 36 2E 20 |) = 2X.2.-8X+6. |
00003B30: 49 4E 20 54 48 49 53 20 43 41 53 45 22 3A 99 00 |IN THIS CASE":..|
00003B40: 71 43 5A 2D 99 22 20 41 3D 32 3B 42 3D 58 91 32 |qCZ-." A=2;B=X.2|
00003B50: 11 3B 43 3D 2D 34 58 20 26 20 44 3D 33 2E 20 4E |.;C=-4X & D=3. N|
00003B60: 4F 57 20 59 4F 55 20 54 52 59 20 4F 4E 45 22 3A |OW YOU TRY ONE":|
00003B70: 99 00 A3 43 64 2D 99 22 20 9B 28 54 4F 20 54 59 |...Cd-." .(TO TY|
00003B80: 50 45 20 58 91 32 11 20 55 53 45 20 5E 20 46 4F |PE X.2. USE ^ FO|
00003B90: 52 20 27 52 41 49 53 45 44 20 54 4F 20 54 48 45 |R 'RAISED TO THE|
00003BA0: 22 3A 99 00 CE 43 6E 2D 99 22 20 50 4F 57 45 52 |":...Cn-." POWER|
00003BB0: 27 2E 20 49 2E 45 2E 20 46 4F 52 20 58 91 32 11 |'. I.E. FOR X.2.|
00003BC0: 20 54 59 50 45 20 58 5E 32 29 9A 22 3A 99 00 00 | TYPE X^2).":...|
00003BD0: 44 78 2D 97 31 39 38 2C 30 3A 85 20 22 20 33 28 |Dx-.198,0:. " 3(|
00003BE0: 58 91 32 11 2B 32 58 2D 34 29 3D 12 D2 D2 D2 D2 |X.2.+2X-4)=.....|
00003BF0: D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 |.....";B1$:.".."|
00003C00: 00 1C 44 82 2D 8B 42 31 24 B2 22 33 58 5E 32 2B |..D.-.B1$."3X^2+|
00003C10: 36 58 2D 31 32 22 89 31 31 37 30 30 00 3B 44 8C |6X-12".11700.;D.|
00003C20: 2D 99 22 20 4E 4F 2C 20 4E 4F 54 20 22 42 31 24 |-." NO, NOT "B1$|
00003C30: 22 20 22 41 31 24 22 2E 22 3A 99 00 69 44 96 2D |" "A1$".":..iD.-|
00003C40: 99 22 20 12 33 58 5E 32 2B 36 58 2D 31 32 92 20 |." .3X^2+6X-12. |
00003C50: 49 53 20 54 48 45 20 43 4F 52 52 45 43 54 20 41 |IS THE CORRECT A|
00003C60: 4E 53 57 45 52 2E 22 3A 99 00 98 44 A0 2D 99 22 |NSWER.":...D.-."|
00003C70: 20 33 28 58 91 32 11 2B 32 58 2D 34 29 20 3D 20 | 3(X.2.+2X-4) = |
00003C80: 33 28 58 91 32 11 29 2B 33 28 32 58 29 2B 33 28 |3(X.2.)+3(2X)+3(|
00003C90: 2D 34 29 20 3D 22 3A 99 00 CC 44 A5 2D 99 22 20 |-4) =":...D.-." |
00003CA0: 33 58 91 32 11 2B 36 58 2D 31 32 20 53 4F 20 59 |3X.2.+6X-12 SO Y|
00003CB0: 4F 55 20 54 59 50 45 20 12 33 58 5E 32 2B 36 58 |OU TYPE .3X^2+6X|
00003CC0: 2D 31 32 92 20 4C 4F 4F 4B 22 3A 99 00 F2 44 AA |-12. LOOK":...D.|
00003CD0: 2D 99 22 20 41 54 20 54 48 49 53 20 41 47 41 49 |-." AT THIS AGAI|
00003CE0: 4E 20 22 41 31 24 22 2E 22 3A 99 3A 89 31 31 35 |N "A1$".":.:.115|
00003CF0: 38 30 00 FC 44 B4 2D 8D 39 30 34 30 00 29 45 BE |80..D.-.9040.)E.|
00003D00: 2D 99 22 20 4F 46 54 45 4E 2C 20 22 41 31 24 22 |-." OFTEN, "A1$"|
00003D10: 20 57 45 20 48 41 56 45 20 50 52 4F 42 4C 45 4D | WE HAVE PROBLEM|
00003D20: 53 20 4C 49 4B 45 22 3A 99 00 61 45 C8 2D 99 22 |S LIKE":..aE.-."|
00003D30: 20 28 32 58 2B 33 29 28 58 2D 31 29 2E 20 53 49 | (2X+3)(X-1). SI|
00003D40: 4E 43 45 20 1E 41 9C 42 9A 3D 9C 42 1E 41 9A 2C |NCE .A.B.=.B.A.,|
00003D50: 20 1E 28 41 2B 42 29 9C 28 43 2B 44 29 9A 22 3A | .(A+B).(C+D).":|
00003D60: 99 00 7E 45 D2 2D 99 A6 32 35 29 22 3D 20 9C 28 |..~E.-..25)"= .(|
00003D70: 43 2B 44 29 1E 28 41 2B 42 29 9A 22 3A 99 00 A0 |C+D).(A+B).":...|
00003D80: 45 DC 2D 99 A6 32 33 29 22 3D 20 9C 28 43 2B 44 |E.-..23)"= .(C+D|
00003D90: 29 1E 41 2B 9C 28 43 2B 44 29 1E 42 9A 22 3A 99 |).A+.(C+D).B.":.|
00003DA0: 00 C3 45 E6 2D 99 A6 32 32 29 22 4F 52 20 1E 41 |..E.-..22)"OR .A|
00003DB0: 9C 28 43 2B 44 29 1E 2B 42 9C 28 43 2B 44 29 9A |.(C+D).+B.(C+D).|
00003DC0: 22 3A 99 00 F7 45 F0 2D 99 22 20 53 4F 22 2C 22 |":...E.-." SO","|
00003DD0: 20 1E 28 41 2B 42 29 9C 28 43 2B 44 29 9A 20 3D | .(A+B).(C+D). =|
00003DE0: 20 20 1E 41 9C 28 43 2B 44 29 1E 2B 42 9C 28 43 | .A.(C+D).+B.(C|
00003DF0: 2B 44 29 9A 22 3A 99 00 31 46 FA 2D 99 22 20 4C |+D).":..1F.-." L|
00003E00: 49 4B 45 57 49 53 45 22 2C 22 1E 28 32 58 2B 33 |IKEWISE",".(2X+3|
00003E10: 29 9C 28 58 2D 31 29 9A 20 3D 20 1E 32 58 9C 28 |).(X-1). = .2X.(|
00003E20: 58 2D 31 29 1E 2B 33 9C 28 58 2D 31 29 9A 22 3A |X-1).+3.(X-1).":|
00003E30: 99 00 69 46 04 2E 99 22 20 3D 20 1E 28 32 58 29 |..iF..." = .(2X)|
00003E40: 9C 28 58 29 9A 2B 1E 28 32 58 29 9C 28 2D 31 29 |.(X).+.(2X).(-1)|
00003E50: 9A 2B 1E 28 33 29 9C 28 58 29 9A 2B 1E 28 33 29 |.+.(3).(X).+.(3)|
00003E60: 9C 28 2D 31 29 9A 22 3A 99 00 6F 46 09 2E 99 00 |.(-1).":..oF....|
00003E70: A5 46 0E 2E 99 22 20 3D 20 32 58 91 32 11 9D 2D |.F..." = 2X.2..-|
00003E80: 34 58 2B 33 58 2D 33 20 3D 20 32 58 91 32 11 9D |4X+3X-3 = 2X.2..|
00003E90: 2D 58 2D 33 2E 20 4E 4F 57 20 59 4F 55 20 54 52 |-X-3. NOW YOU TR|
00003EA0: 59 3A 22 3A 99 00 C8 46 13 2E 99 3A 99 22 20 9B |Y:":...F...:." .|
00003EB0: 28 55 53 45 20 58 5E 32 20 46 4F 52 20 58 91 32 |(USE X^2 FOR X.2|
00003EC0: 11 29 9A 22 3A 99 3A 99 00 F8 46 18 2E 97 31 39 |.).":.:...F...19|
00003ED0: 38 2C 30 3A 85 20 22 20 28 33 58 2D 32 29 28 58 |8,0:. " (3X-2)(X|
00003EE0: 2B 31 29 20 3D 20 12 D2 D2 D2 D2 D2 D2 D2 22 3B |+1) = ........";|
00003EF0: 42 31 24 3A 99 22 92 22 00 12 47 22 2E 8B 42 31 |B1$:."."..G"..B1|
00003F00: 24 B2 22 33 58 5E 32 2B 58 2D 32 22 89 31 31 38 |$."3X^2+X-2".118|
00003F10: 37 30 00 1B 47 27 2E 99 22 93 22 00 4A 47 2C 2E |70..G'..".".JG,.|
00003F20: 99 22 20 4E 4F 2C 20 59 4F 55 20 53 48 4F 55 4C |." NO, YOU SHOUL|
00003F30: 44 20 48 41 56 45 20 54 59 50 45 44 20 12 33 58 |D HAVE TYPED .3X|
00003F40: 5E 32 2B 58 2D 32 92 22 3A 99 00 50 47 31 2E 99 |^2+X-2.":..PG1..|
00003F50: 00 7F 47 36 2E 99 22 20 1E 28 33 58 2D 32 29 9C |..G6.." .(3X-2).|
00003F60: 28 58 2B 31 29 9A 3D 1E 33 58 9C 28 58 2B 31 29 |(X+1).=.3X.(X+1)|
00003F70: 1E 2D 32 9C 28 58 2B 31 29 9A 20 3D 22 3A 99 00 |.-2.(X+1). =":..|
00003F80: 85 47 3B 2E 99 00 BA 47 40 2E 99 22 20 33 58 91 |.G;....G@.." 3X.|
00003F90: 32 11 2B 33 58 2D 32 58 2D 32 20 3D 20 33 58 91 |2.+3X-2X-2 = 3X.|
00003FA0: 32 11 2B 58 2D 32 20 53 4F 20 12 33 58 5E 32 2B |2.+X-2 SO .3X^2+|
00003FB0: 58 2D 32 92 20 49 53 22 3A 99 00 C0 47 45 2E 99 |X-2. IS":...GE..|
00003FC0: 00 EE 47 4A 2E 99 22 20 43 4F 52 52 45 43 54 2E |..GJ.." CORRECT.|
00003FD0: 20 4C 45 54 27 53 20 47 4F 20 42 41 43 4B 20 41 | LET'S GO BACK A|
00003FE0: 20 42 49 54 20 22 41 31 24 22 2E 22 3A 99 00 21 | BIT "A1$".":..!|
00003FF0: 48 54 2E 99 22 20 52 45 4D 45 4D 42 45 52 2C 20 |HT.." REMEMBER, |
00004000: 49 46 20 59 4F 55 20 57 41 4E 54 20 54 4F 20 53 |IF YOU WANT TO S|
00004010: 49 4D 50 4C 49 46 59 22 3A 99 3A 89 31 31 34 30 |IMPLIFY":.:.1140|
00004020: 30 00 2B 48 5E 2E 8D 39 30 30 30 00 5D 48 60 2E |0.+H^..9000.]H`.|
00004030: 97 31 39 38 2C 30 3A 85 20 22 20 41 4E 44 20 28 |.198,0:. " AND (|
00004040: 58 2B 32 29 91 32 11 3D 20 12 D2 D2 D2 D2 D2 D2 |X+2).2.= .......|
00004050: D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 00 77 48 |..";B1$:."..".wH|
00004060: 62 2E 8B 42 31 24 B2 22 58 5E 32 2B 34 58 2B 34 |b..B1$."X^2+4X+4|
00004070: 22 89 31 31 38 38 38 00 A6 48 64 2E 99 22 20 4E |".11888..Hd.." N|
00004080: 4F 2C 20 4E 4F 54 20 22 42 31 24 22 20 12 58 5E |O, NOT "B1$" .X^|
00004090: 32 2B 34 58 2B 34 92 20 49 53 20 52 49 47 48 54 |2+4X+4. IS RIGHT|
000040A0: 2E 22 3A 99 3A 99 00 D5 48 66 2E 99 22 20 28 58 |.":.:...Hf.." (X|
000040B0: 2B 32 29 91 32 11 3D 28 58 2B 32 29 28 58 2B 32 |+2).2.=(X+2)(X+2|
000040C0: 29 3D 58 28 58 2B 32 29 2B 32 28 58 2B 32 29 3D |)=X(X+2)+2(X+2)=|
000040D0: 22 3A 99 3A 99 00 07 49 68 2E 99 22 20 58 91 32 |":.:...Ih.." X.2|
000040E0: 11 2B 32 58 2B 32 58 2B 32 91 32 11 3D 58 91 32 |.+2X+2X+2.2.=X.2|
000040F0: 11 2B 34 58 2B 34 20 53 4F 20 59 4F 55 20 53 48 |.+4X+4 SO YOU SH|
00004100: 4F 55 4C 44 22 3A 99 00 40 49 6A 2E 99 22 20 54 |OULD":..@Ij.." T|
00004110: 59 50 45 20 12 58 5E 32 2B 34 58 2B 34 92 20 49 |YPE .X^2+4X+4. I|
00004120: 46 20 59 4F 55 20 57 41 4E 54 20 54 4F 20 53 49 |F YOU WANT TO SI|
00004130: 4D 50 4C 49 46 59 22 3A 99 3A 89 31 31 34 30 30 |MPLIFY":.:.11400|
00004140: 00 4A 49 70 2E 8D 39 30 30 30 00 7A 49 71 2E 99 |.JIp..9000.zIq..|
00004150: 22 20 42 45 46 4F 52 45 20 57 45 20 41 44 44 20 |" BEFORE WE ADD |
00004160: 26 20 53 55 42 54 52 41 43 54 20 45 58 50 52 45 |& SUBTRACT EXPRE|
00004170: 53 53 49 4F 4E 53 2C 22 3A 99 00 A6 49 72 2E 99 |SSIONS,":...Ir..|
00004180: 22 20 22 41 31 24 22 2C 20 52 45 43 41 4C 4C 20 |" "A1$", RECALL |
00004190: 54 48 41 54 20 2D 28 41 2B 42 2B 43 29 20 4D 45 |THAT -(A+B+C) ME|
000041A0: 41 4E 53 22 3A 99 00 D7 49 7C 2E 99 22 20 2D 31 |ANS":...I|.." -1|
000041B0: 20 54 49 4D 45 53 20 28 41 2B 42 2B 43 29 20 3D | TIMES (A+B+C) =|
000041C0: 20 28 2D 41 29 2B 28 2D 42 29 2B 28 2D 43 29 20 | (-A)+(-B)+(-C) |
000041D0: 54 48 41 54 22 3A 99 00 05 4A 86 2E 99 22 20 49 |THAT":...J..." I|
000041E0: 53 2C 20 2D 41 2D 42 2D 43 2E 20 53 4F 20 2D 28 |S, -A-B-C. SO -(|
000041F0: 41 2D 42 2B 43 29 3D 2D 41 2B 42 2D 43 2E 20 4E |A-B+C)=-A+B-C. N|
00004200: 4F 57 22 3A 99 00 3B 4A 90 2E 97 31 39 38 2C 30 |OW":..;J...198,0|
00004210: 3A 85 20 22 20 49 54 53 20 59 4F 55 52 20 54 55 |:. " ITS YOUR TU|
00004220: 52 4E 2E 20 2D 28 31 2B 34 2D 33 29 20 3D 20 12 |RN. -(1+4-3) = .|
00004230: D2 22 3B 42 31 24 3A 99 22 92 22 00 79 4A 95 2E |.";B1$:.".".yJ..|
00004240: 8B 42 31 24 B2 22 2D 31 2D 34 2B 33 22 A7 85 20 |.B1$."-1-4+3".. |
00004250: 22 20 1E 43 4F 52 52 45 43 54 2C 20 9A 41 4E 44 |" .CORRECT, .AND|
00004260: 20 54 48 49 53 20 45 51 55 41 4C 53 20 12 D2 22 | THIS EQUALS .."|
00004270: 3B 42 31 24 3A 99 22 92 22 00 8D 4A 9A 2E 8B 42 |;B1$:."."..J...B|
00004280: 31 24 B2 22 2D 32 22 89 31 31 39 36 30 00 96 4A |1$."-2".11960..J|
00004290: 9F 2E 99 22 93 22 00 C9 4A A4 2E 99 22 20 4E 4F |..."."..J..." NO|
000042A0: 2C 20 12 2D 32 92 20 49 53 20 43 4F 52 52 45 43 |, .-2. IS CORREC|
000042B0: 54 2E 20 2D 28 31 2B 34 2D 33 29 3D 20 2D 31 28 |T. -(1+4-3)= -1(|
000042C0: 31 2B 34 2D 33 29 22 3A 99 00 F7 4A AE 2E 99 22 |1+4-3)":...J..."|
000042D0: 20 57 48 49 43 48 20 49 53 20 28 2D 31 29 28 31 | WHICH IS (-1)(1|
000042E0: 29 2B 28 2D 31 29 28 34 29 2B 28 2D 31 29 28 2D |)+(-1)(4)+(-1)(-|
000042F0: 33 29 20 3D 22 3A 99 00 2F 4B B3 2E 99 22 20 2D |3) =":../K..." -|
00004300: 31 2D 34 2B 33 20 3D 20 12 2D 32 92 2E 20 4F 4B |1-4+3 = .-2.. OK|
00004310: 20 4C 45 54 27 53 20 54 52 59 20 54 48 49 53 20 | LET'S TRY THIS |
00004320: 41 47 41 49 4E 22 3A 99 3A 89 31 31 38 39 30 00 |AGAIN":.:.11890.|
00004330: 39 4B B8 2E 8D 39 30 30 30 00 66 4B C2 2E 97 31 |9K...9000.fK...1|
00004340: 39 38 2C 30 3A 85 20 22 20 53 4F 20 35 58 2D 28 |98,0:. " SO 5X-(|
00004350: 34 58 2D 32 29 20 3D 20 12 D2 D2 D2 22 3B 42 31 |4X-2) = ....";B1|
00004360: 24 3A 99 22 92 22 00 7B 4B CC 2E 8B 42 31 24 B2 |$:.".".{K...B1$.|
00004370: 22 58 2B 32 22 89 31 32 30 32 30 00 84 4B D1 2E |"X+2".12020..K..|
00004380: 99 22 93 22 00 B6 4B D6 2E 99 22 20 4E 4F 2C 20 |."."..K..." NO, |
00004390: 12 58 2B 32 92 20 49 53 20 43 4F 52 52 45 43 54 |.X+2. IS CORRECT|
000043A0: 2E 20 35 58 2D 28 34 58 2D 32 29 3D 35 58 2D 34 |. 5X-(4X-2)=5X-4|
000043B0: 58 2B 32 22 3A 99 00 EC 4B E0 2E 99 22 20 3D 20 |X+2":...K..." = |
000043C0: 12 58 2B 32 92 2E 20 57 45 20 48 41 44 20 42 45 |.X+2.. WE HAD BE|
000043D0: 54 54 45 52 20 52 45 56 49 45 57 20 22 41 31 24 |TTER REVIEW "A1$|
000043E0: 22 2E 22 3A 99 3A 89 31 31 38 36 30 00 F6 4B F4 |".":.:.11860..K.|
000043F0: 2E 8D 39 30 30 30 00 27 4C FE 2E 99 22 20 4E 4F |..9000.'L..." NO|
00004400: 57 20 54 52 59 20 4F 4E 45 20 53 4C 49 47 48 54 |W TRY ONE SLIGHT|
00004410: 4C 59 20 4D 4F 52 45 20 43 4F 4D 50 4C 49 43 41 |LY MORE COMPLICA|
00004420: 54 45 44 2E 22 3A 99 00 4C 4C 08 2F 99 22 20 53 |TED.":..LL./." S|
00004430: 49 4D 50 4C 49 46 59 3A 20 33 58 2D 32 59 2B 37 |IMPLIFY: 3X-2Y+7|
00004440: 2D 28 58 2B 32 59 2D 33 29 22 3A 99 00 70 4C 12 |-(X+2Y-3)":..pL.|
00004450: 2F 97 31 39 38 2C 30 3A 85 20 22 20 12 D2 D2 D2 |/.198,0:. " ....|
00004460: D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 |.....";B1$:.".."|
00004470: 00 8A 4C 1C 2F 8B 42 31 24 B2 22 32 58 2D 34 59 |..L./.B1$."2X-4Y|
00004480: 2B 31 30 22 89 31 32 30 38 30 00 B1 4C 21 2F 99 |+10".12080..L!/.|
00004490: 22 20 12 32 58 2D 34 59 2B 31 30 92 20 49 53 20 |" .2X-4Y+10. IS |
000044A0: 52 49 47 48 54 2C 20 4E 4F 54 20 22 42 31 24 3A |RIGHT, NOT "B1$:|
000044B0: 99 00 E7 4C 26 2F 99 22 20 33 58 2D 32 59 2B 37 |...L&/." 3X-2Y+7|
000044C0: 2D 28 58 2B 32 59 2D 33 29 20 3D 20 9C 33 58 9A |-(X+2Y-3) = .3X.|
000044D0: 2D 1E 32 59 9A 2B 37 2D 9C 58 9A 2D 1E 32 59 9A |-.2Y.+7-.X.-.2Y.|
000044E0: 2D 33 20 3D 22 3A 99 00 29 4D 2B 2F 99 22 20 9C |-3 =":..)M+/." .|
000044F0: 33 58 9A 2D 9C 58 9A 2D 1E 32 59 9A 2D 1E 32 59 |3X.-.X.-.2Y.-.2Y|
00004500: 9A 2B 37 2B 33 20 3D 20 12 32 58 2D 34 59 2B 31 |.+7+3 = .2X-4Y+1|
00004510: 30 92 2E 20 54 4F 20 53 49 4D 50 4C 49 46 59 22 |0.. TO SIMPLIFY"|
00004520: 3A 99 3A 89 31 31 34 30 30 00 33 4D 30 2F 8D 39 |:.:.11400.3M0/.9|
00004530: 30 30 30 00 5E 4D 3A 2F 99 22 20 41 53 20 49 20 |000.^M:/." AS I |
00004540: 4D 45 4E 54 49 4F 4E 45 44 2C 20 22 41 31 24 22 |MENTIONED, "A1$"|
00004550: 2C 20 54 48 45 52 45 20 41 52 45 22 3A 99 00 8E |, THERE ARE":...|
00004560: 4D 44 2F 99 22 20 4C 41 57 53 20 46 4F 52 20 44 |MD/." LAWS FOR D|
00004570: 45 41 4C 49 4E 47 20 57 49 54 48 20 45 58 50 4F |EALING WITH EXPO|
00004580: 4E 45 4E 54 53 28 50 4F 57 45 52 53 29 22 00 C3 |NENTS(POWERS)"..|
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00007CB0: 53 49 47 4E 53 20 49 4E 20 42 4F 54 48 20 46 41 |SIGNS IN BOTH FA|
00007CC0: 43 54 4F 52 53 20 41 52 45 20 12 D2 22 3B 42 31 |CTORS ARE ..";B1|
00007CD0: 24 3A 99 22 92 22 00 E7 85 96 3C 8B 42 31 24 B2 |$:."."....<.B1$.|
00007CE0: 22 2B 22 89 31 35 35 35 30 00 F0 85 9B 3C 99 22 |"+".15550....<."|
00007CF0: 93 22 00 26 86 A0 3C 99 22 20 4E 4F 20 4E 4F 54 |.".&..<." NO NOT|
00007D00: 20 22 42 31 24 22 2C 20 12 2B 92 20 49 53 20 43 | "B1$", .+. IS C|
00007D10: 4F 52 52 45 43 54 20 28 58 9B 2B 9A 50 29 28 58 |ORRECT (X.+.P)(X|
00007D20: 9B 2B 9A 51 29 22 3A 99 00 53 86 AA 3C 99 22 20 |.+.Q)":..S..<." |
00007D30: 3D 28 58 29 28 58 29 9B 2B 9A 28 58 29 28 51 29 |=(X)(X).+.(X)(Q)|
00007D40: 9B 2B 9A 28 58 29 28 50 29 9B 2B 9A 28 50 29 28 |.+.(X)(P).+.(P)(|
00007D50: 51 29 22 3A 99 00 87 86 B4 3C 99 22 20 3D 58 91 |Q)":.....<." =X.|
00007D60: 32 11 9B 2B 9A 28 51 2B 50 29 58 9B 2B 9A 50 51 |2..+.(Q+P)X.+.PQ|
00007D70: 2E 20 4C 45 54 27 53 20 52 45 56 49 45 57 3A 22 |. LET'S REVIEW:"|
00007D80: 3A 99 3A 89 31 35 32 31 30 00 91 86 BE 3C 8D 39 |:.:.15210....<.9|
00007D90: 30 30 30 00 C7 86 C8 3C 99 22 9F 33 9A 20 49 46 |000....<.".3. IF|
00007DA0: 20 9C 42 20 49 53 20 4E 45 47 41 54 49 56 45 9A | .B IS NEGATIVE.|
00007DB0: 20 26 20 1E 43 20 49 53 20 50 4F 53 49 54 49 56 | & .C IS POSITIV|
00007DC0: 45 9A 20 54 48 45 22 3A 99 00 F5 86 D2 3C 99 22 |E. THE":.....<."|
00007DD0: 20 53 49 47 4E 53 20 49 4E 20 54 48 45 20 46 41 | SIGNS IN THE FA|
00007DE0: 43 54 4F 52 53 20 41 52 45 20 9B 42 4F 54 48 9A |CTORS ARE .BOTH.|
00007DF0: 20 12 2D 92 22 3A 99 00 32 87 DC 3C 99 22 20 28 | .-.":..2..<." (|
00007E00: 58 9B 2D 9A 50 29 28 58 9B 2D 9A 51 29 3D 58 91 |X.-.P)(X.-.Q)=X.|
00007E10: 32 11 9B 2D 9A 28 50 2B 51 29 58 9F 2B 9A 50 51 |2..-.(P+Q)X.+.PQ|
00007E20: 20 5B 41 3D 31 3B 42 3D 9B 2D 9A 28 50 2B 51 29 | [A=1;B=.-.(P+Q)|
00007E30: 3B 22 3A 99 00 67 87 E6 3C 99 22 20 43 3D 9F 2B |;":..g..<." C=.+|
00007E40: 9A 50 51 5D 20 53 4F 20 54 4F 20 46 41 43 54 4F |.PQ] SO TO FACTO|
00007E50: 52 49 53 45 20 58 91 32 11 9B 2D 9A 35 58 9B 2B |RISE X.2..-.5X.+|
00007E60: 9A 36 20 54 48 45 22 3A 99 00 9E 87 F0 3C 97 31 |.6 THE":.....<.1|
00007E70: 39 38 2C 30 3A 85 20 22 20 53 49 47 4E 53 20 49 |98,0:. " SIGNS I|
00007E80: 4E 20 42 4F 54 48 20 46 41 43 54 4F 52 53 20 41 |N BOTH FACTORS A|
00007E90: 52 45 20 12 D2 22 3B 42 31 24 3A 99 22 92 93 22 |RE ..";B1$:.".."|
00007EA0: 00 B1 87 FA 3C 8B 42 31 24 B2 22 2D 22 89 31 35 |....<.B1$."-".15|
00007EB0: 36 34 30 00 E3 87 04 3D 99 22 20 4E 4F 2C 20 54 |640....=." NO, T|
00007EC0: 48 45 59 20 41 52 45 20 42 4F 54 48 20 12 2D 92 |HEY ARE BOTH .-.|
00007ED0: 2E 20 28 58 9B 2D 9A 50 29 28 58 9B 2D 9A 51 29 |. (X.-.P)(X.-.Q)|
00007EE0: 20 3D 22 3A 99 00 1F 88 0E 3D 99 22 20 28 58 29 | =":.....=." (X)|
00007EF0: 28 58 29 9B 2D 9A 51 58 9B 2D 9A 50 58 9B 2B 9A |(X).-.QX.-.PX.+.|
00007F00: 50 51 20 3D 20 58 91 32 11 9B 2D 9A 28 51 2B 50 |PQ = X.2..-.(Q+P|
00007F10: 29 58 9B 2B 9A 50 51 2E 20 4C 45 54 27 53 22 3A |)X.+.PQ. LET'S":|
00007F20: 99 00 4B 88 13 3D 99 22 20 53 54 41 52 54 20 41 |..K..=." START A|
00007F30: 47 41 49 4E 20 4F 4E 20 54 48 49 53 20 22 41 31 |GAIN ON THIS "A1|
00007F40: 24 22 2E 22 3A 99 3A 89 31 35 32 31 30 00 55 88 |$".":.:.15210.U.|
00007F50: 18 3D 8D 39 30 30 30 00 88 88 22 3D 99 22 9F 34 |.=.9000..."=.".4|
00007F60: 9A 20 49 46 20 9B 43 9A 20 49 53 20 9B 4E 45 47 |. IF .C. IS .NEG|
00007F70: 41 54 49 56 45 9A 20 54 48 45 20 53 49 47 4E 53 |ATIVE. THE SIGNS|
00007F80: 20 49 4E 20 54 48 45 22 3A 99 00 BB 88 2C 3D 99 | IN THE":....,=.|
00007F90: 22 20 46 41 43 54 4F 52 53 20 41 52 45 20 12 44 |" FACTORS ARE .D|
00007FA0: 49 46 46 45 52 45 4E 54 92 20 28 58 9B 2B 9A 50 |IFFERENT. (X.+.P|
00007FB0: 29 28 58 9B 2D 9A 51 29 20 3D 22 3A 99 00 F2 88 |)(X.-.Q) =":....|
00007FC0: 36 3D 99 22 20 58 91 32 11 2B 28 50 2D 51 29 58 |6=." X.2.+(P-Q)X|
00007FD0: 9B 2D 9A 50 51 20 5B 41 3D 31 3B 42 3D 28 50 2D |.-.PQ [A=1;B=(P-|
00007FE0: 51 29 3B 43 3D 9B 2D 9A 50 51 5D 20 53 4F 20 54 |Q);C=.-.PQ] SO T|
00007FF0: 4F 22 3A 99 00 22 89 40 3D 99 22 20 46 41 43 54 |O":..".@=." FACT|
00008000: 4F 52 49 53 45 20 58 91 32 11 2B 58 9B 2D 9A 36 |ORISE X.2.+X.-.6|
00008010: 20 54 48 45 20 53 49 47 4E 53 20 49 4E 20 54 48 | THE SIGNS IN TH|
00008020: 45 22 3A 99 00 51 89 4A 3D 97 31 39 38 2C 30 3A |E":..Q.J=.198,0:|
00008030: 85 22 20 46 41 43 54 4F 52 53 20 41 52 45 20 12 |." FACTORS ARE .|
00008040: D2 D2 D2 D2 D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 |.........";B1$:.|
00008050: 22 92 22 00 6C 89 54 3D 8B 42 31 24 B2 22 44 49 |".".l.T=.B1$."DI|
00008060: 46 46 45 52 45 4E 54 22 89 31 35 37 33 30 00 A2 |FFERENT".15730..|
00008070: 89 5E 3D 99 22 20 4E 4F 2C 20 54 48 45 20 53 49 |.^=." NO, THE SI|
00008080: 47 4E 53 20 41 52 45 20 12 44 49 46 46 45 52 45 |GNS ARE .DIFFERE|
00008090: 4E 54 92 2E 20 28 58 9B 2B 9A 50 29 28 58 9B 2D |NT.. (X.+.P)(X.-|
000080A0: 9A 51 29 22 00 E2 89 68 3D 99 22 20 3D 28 58 29 |.Q)"...h=." =(X)|
000080B0: 28 58 29 2D 51 58 2B 50 58 9B 2D 9A 50 51 20 3D |(X)-QX+PX.-.PQ =|
000080C0: 20 58 91 32 11 2B 28 50 2D 51 29 9B 2D 9A 50 51 | X.2.+(P-Q).-.PQ|
000080D0: 20 9F 52 45 56 49 45 57 3A 9A 22 3A 99 3A 89 31 | .REVIEW:.":.:.1|
000080E0: 35 32 31 30 00 EC 89 72 3D 8D 39 30 34 30 00 1E |5210...r=.9040..|
000080F0: 8A 7C 3D 99 22 9F 35 9A 20 49 46 20 41 3D 31 2C |.|=.".5. IF A=1,|
00008100: 20 54 48 45 20 53 45 43 4F 4E 44 20 54 45 52 4D | THE SECOND TERM|
00008110: 53 20 4F 46 20 54 48 45 20 46 41 43 2D 22 3A 99 |S OF THE FAC-":.|
00008120: 00 48 8A 86 3D 99 22 20 54 4F 52 53 20 48 41 56 |.H..=." TORS HAV|
00008130: 45 20 41 20 53 55 4D 3D 42 20 26 20 41 20 50 52 |E A SUM=B & A PR|
00008140: 4F 44 55 43 54 3D 43 22 3A 99 00 78 8A 90 3D 99 |ODUCT=C":..x..=.|
00008150: 22 20 28 49 4E 20 41 58 91 32 11 2B 42 58 2B 43 |" (IN AX.2.+BX+C|
00008160: 29 20 49 2E 45 2E 20 28 58 2B 9B 50 9A 29 28 58 |) I.E. (X+.P.)(X|
00008170: 2B 9B 51 9A 29 20 3D 22 3A 99 00 A3 8A 9A 3D 99 |+.Q.) =":.....=.|
00008180: 22 20 58 91 32 11 2B 9B 28 50 2B 51 29 9A 58 2B |" X.2.+.(P+Q).X+|
00008190: 9B 50 51 9A 20 53 4F 20 22 41 31 24 22 20 43 4F |.PQ. SO "A1$" CO|
000081A0: 4E 2D 22 3A 99 00 D9 8A A4 3D 99 22 20 53 49 44 |N-":.....=." SID|
000081B0: 45 52 49 4E 47 20 58 91 32 11 2B 12 35 92 58 2B |ERING X.2.+.5.X+|
000081C0: 12 36 92 2C 20 54 48 45 20 53 45 43 4F 4E 44 20 |.6., THE SECOND |
000081D0: 54 45 52 4D 53 20 4F 46 22 3A 99 00 0E 8B AE 3D |TERMS OF":.....=|
000081E0: 97 31 39 38 2C 30 3A 85 22 20 54 48 45 20 46 41 |.198,0:." THE FA|
000081F0: 43 54 4F 52 53 20 48 41 56 45 20 41 20 53 55 4D |CTORS HAVE A SUM|
00008200: 20 4F 46 20 12 D2 22 3B 42 31 24 3A 99 22 92 22 | OF ..";B1$:."."|
00008210: 00 35 8B B8 3D 8B 42 31 24 B2 22 35 22 B0 42 31 |.5..=.B1$."5".B1|
00008220: 24 B2 22 32 2B 33 22 B0 42 31 24 B2 22 33 2B 32 |$."2+3".B1$."3+2|
00008230: 22 89 31 35 38 34 30 00 63 8B C2 3D 99 22 93 22 |".15840.c..=."."|
00008240: 3A 99 22 20 4E 4F 2C 20 4E 4F 54 20 22 42 31 24 |:." NO, NOT "B1$|
00008250: 22 2E 20 12 35 92 20 49 53 20 43 4F 52 52 45 43 |". .5. IS CORREC|
00008260: 54 2E 22 3A 99 00 9E 8B CC 3D 99 22 20 28 58 2B |T.":.....=." (X+|
00008270: 33 29 28 58 2B 32 29 3D 58 91 32 11 2B 12 28 32 |3)(X+2)=X.2.+.(2|
00008280: 2B 33 29 92 58 2B 36 2E 20 4C 45 54 27 53 20 52 |+3).X+6. LET'S R|
00008290: 45 56 49 45 57 2E 22 3A 99 3A 89 31 35 32 31 30 |EVIEW.":.:.15210|
000082A0: 00 A8 8B E0 3D 8D 39 30 30 30 00 DF 8B EA 3D 97 |....=.9000....=.|
000082B0: 31 39 38 2C 30 3A 85 20 22 20 20 20 20 20 20 20 |198,0:. " |
000082C0: 20 20 20 41 4E 44 20 41 20 50 52 4F 44 55 43 54 | AND A PRODUCT|
000082D0: 20 4F 46 20 12 D2 22 3B 42 31 24 3A 99 22 92 93 | OF ..";B1$:."..|
000082E0: 22 00 F2 8B F4 3D 8B 42 31 24 B2 22 36 22 89 31 |"....=.B1$."6".1|
000082F0: 35 39 30 30 00 25 8C FE 3D 99 22 20 4E 4F 20 4E |5900.%..=." NO N|
00008300: 4F 54 20 22 42 31 24 22 2E 20 12 36 92 20 49 53 |OT "B1$". .6. IS|
00008310: 20 43 4F 52 52 45 43 54 2E 20 28 58 2B 33 29 28 | CORRECT. (X+3)(|
00008320: 58 2B 32 29 22 3A 99 00 60 8C 08 3E 99 22 20 3D |X+2)":..`..>." =|
00008330: 58 91 32 11 2B 35 58 2B 12 28 32 29 28 33 29 92 |X.2.+5X+.(2)(3).|
00008340: 2C 20 4C 45 54 27 53 20 52 45 56 49 45 57 20 54 |, LET'S REVIEW T|
00008350: 48 49 53 20 50 41 52 54 22 3A 99 3A 89 31 35 32 |HIS PART":.:.152|
00008360: 31 30 00 6A 8C 1C 3E 8D 39 30 30 30 00 9A 8C 26 |10.j..>.9000...&|
00008370: 3E 99 22 9F 36 9A 20 9B 57 52 49 54 45 20 44 4F |>.".6. .WRITE DO|
00008380: 57 4E 20 54 48 45 20 46 41 43 54 4F 52 53 20 26 |WN THE FACTORS &|
00008390: 20 4D 55 4C 54 49 50 4C 59 22 3A 99 00 C9 8C 30 | MULTIPLY":....0|
000083A0: 3E 99 22 20 54 48 45 4D 20 4F 55 54 20 54 4F 20 |>." THEM OUT TO |
000083B0: 43 48 45 43 4B 21 9A 20 4F 4B 2C 20 4C 45 54 53 |CHECK!. OK, LETS|
000083C0: 20 4C 4F 4F 4B 20 41 54 22 3A 99 00 F6 8C 3A 3E | LOOK AT":....:>|
000083D0: 99 22 20 41 4E 20 9F 45 58 41 4D 50 4C 45 3A 9A |." AN .EXAMPLE:.|
000083E0: 20 46 41 43 54 4F 52 49 53 45 20 58 91 32 11 2B | FACTORISE X.2.+|
000083F0: 39 58 2B 32 30 22 3A 99 00 06 8D 3F 3E 81 4C B2 |9X+20":....?>.L.|
00008400: 31 A4 34 30 30 30 3A 82 00 1C 8D 44 3E 99 22 20 |1.4000:....D>." |
00008410: 9F 53 4F 4C 55 54 49 4F 4E 3A 9A 22 3A 99 00 3E |.SOLUTION:.":..>|
00008420: 8D 4E 3E 99 22 9F 31 9A 20 28 58 20 20 29 28 58 |.N>.".1. (X )(X|
00008430: 20 20 29 20 53 49 4E 43 45 20 41 3D 31 22 3A 99 | ) SINCE A=1":.|
00008440: 00 4E 8D 53 3E 81 4C B2 31 A4 34 30 30 30 3A 82 |.N.S>.L.1.4000:.|
00008450: 00 7D 8D 58 3E 99 22 9F 32 9A 20 28 58 2B 20 29 |.}.X>.".2. (X+ )|
00008460: 28 58 2B 20 29 20 53 49 4E 43 45 20 42 3D 9B 2B |(X+ ) SINCE B=.+|
00008470: 9A 39 20 26 20 43 3D 9B 2B 9A 32 30 22 3A 99 00 |.9 & C=.+.20":..|
00008480: 8D 8D 5D 3E 81 4C B2 31 A4 34 30 30 30 3A 82 00 |..]>.L.1.4000:..|
00008490: BD 8D 62 3E 99 22 9F 33 9A 20 28 58 2B 35 29 28 |..b>.".3. (X+5)(|
000084A0: 58 2B 34 29 20 53 49 4E 43 45 20 34 2B 35 3D 39 |X+4) SINCE 4+5=9|
000084B0: 20 26 20 28 34 29 28 35 29 3D 32 30 22 3A 99 00 | & (4)(5)=20":..|
000084C0: CD 8D 67 3E 81 4C B2 31 A4 34 30 30 30 3A 82 00 |..g>.L.1.4000:..|
000084D0: F9 8D 6C 3E 99 22 20 4E 4F 57 20 59 4F 55 20 54 |..l>." NOW YOU T|
000084E0: 52 59 3A 20 46 41 43 54 4F 52 49 53 45 20 58 91 |RY: FACTORISE X.|
000084F0: 32 11 2B 37 58 2B 31 32 22 3A 99 00 1F 8E 76 3E |2.+7X+12":....v>|
00008500: 97 31 39 38 2C 30 3A 85 20 22 20 12 28 D2 D2 D2 |.198,0:. " .(...|
00008510: 29 28 D2 D2 D2 29 22 3B 42 31 24 3A 99 22 92 93 |)(...)";B1$:."..|
00008520: 22 00 4C 8E 80 3E 8B 42 31 24 B2 22 28 58 2B 34 |".L..>.B1$."(X+4|
00008530: 29 28 58 2B 33 29 22 B0 42 31 24 B2 22 28 58 2B |)(X+3)".B1$."(X+|
00008540: 33 29 28 58 2B 34 29 22 89 31 36 30 34 30 00 79 |3)(X+4)".16040.y|
00008550: 8E 8A 3E 99 22 20 4E 4F 20 4E 4F 54 20 22 42 31 |..>." NO NOT "B1|
00008560: 24 22 20 12 28 58 2B 34 29 28 58 2B 33 29 92 20 |$" .(X+4)(X+3). |
00008570: 49 53 20 52 49 47 48 54 22 3A 99 00 A9 8E 94 3E |IS RIGHT":.....>|
00008580: 99 22 20 28 58 2B 34 29 28 58 2B 33 29 3D 58 91 |." (X+4)(X+3)=X.|
00008590: 32 11 2B 33 58 2B 34 58 2B 31 32 20 3D 20 58 91 |2.+3X+4X+12 = X.|
000085A0: 32 11 2B 37 58 2B 31 32 22 3A 99 00 DB 8E 9E 3E |2.+7X+12":.....>|
000085B0: 99 22 20 57 45 20 48 41 44 20 42 45 54 54 45 52 |." WE HAD BETTER|
000085C0: 20 52 45 56 49 45 57 20 54 48 49 53 20 22 41 31 | REVIEW THIS "A1|
000085D0: 24 22 2E 22 3A 99 3A 89 31 35 32 31 30 00 E5 8E |$".":.:.15210...|
000085E0: A8 3E 8D 39 30 34 30 00 10 8F B2 3E 99 22 20 9F |.>.9040....>." .|
000085F0: 45 58 41 4D 50 4C 45 20 32 3A 9A 20 46 41 43 54 |EXAMPLE 2:. FACT|
00008600: 4F 52 49 53 45 20 58 91 32 11 2D 35 58 2B 36 22 |ORISE X.2.-5X+6"|
00008610: 3A 99 00 32 8F BC 3E 99 22 9F 31 9A 20 28 58 20 |:..2..>.".1. (X |
00008620: 20 29 28 58 20 20 29 20 53 49 4E 43 45 20 41 3D | )(X ) SINCE A=|
00008630: 31 22 3A 99 00 42 8F C1 3E 81 4C B2 31 A4 34 30 |1":..B..>.L.1.40|
00008640: 30 30 3A 82 00 74 8F C6 3E 99 22 9F 32 9A 20 28 |00:..t..>.".2. (|
00008650: 58 9B 2D 9A 20 29 28 58 9B 2D 9A 20 29 20 53 49 |X.-. )(X.-. ) SI|
00008660: 4E 43 45 20 42 3D 9B 2D 9A 35 20 26 20 43 3D 9B |NCE B=.-.5 & C=.|
00008670: 2B 9A 36 22 3A 99 00 84 8F CB 3E 81 4C B2 31 A4 |+.6":.....>.L.1.|
00008680: 34 30 30 30 3A 82 00 B2 8F D0 3E 99 22 9F 33 9A |4000:.....>.".3.|
00008690: 20 28 58 2D 33 29 28 58 2D 32 29 20 53 49 4E 43 | (X-3)(X-2) SINC|
000086A0: 45 20 28 2D 33 29 2B 28 2D 32 29 3D 2D 35 20 26 |E (-3)+(-2)=-5 &|
000086B0: 20 22 3A 99 00 C9 8F DA 3E 99 22 20 28 2D 33 29 | ":.....>." (-3)|
000086C0: 28 2D 32 29 3D 36 2E 20 22 3A 99 00 D9 8F DF 3E |(-2)=6. ":.....>|
000086D0: 81 4C B2 31 A4 34 30 30 30 3A 82 00 05 90 E4 3E |.L.1.4000:.....>|
000086E0: 99 22 20 4E 4F 57 20 59 4F 55 20 54 52 59 2C 20 |." NOW YOU TRY, |
000086F0: 46 41 43 54 4F 52 49 53 45 20 58 91 32 11 2D 37 |FACTORISE X.2.-7|
00008700: 58 2B 31 32 22 3A 99 00 2B 90 EE 3E 97 31 39 38 |X+12":..+..>.198|
00008710: 2C 30 3A 85 20 22 20 12 28 D2 D2 D2 29 28 D2 D2 |,0:. " .(...)(..|
00008720: D2 29 22 3B 42 31 24 3A 99 22 92 93 22 00 58 90 |.)";B1$:."..".X.|
00008730: F8 3E 8B 42 31 24 B2 22 28 58 2D 34 29 28 58 2D |.>.B1$."(X-4)(X-|
00008740: 33 29 22 B0 42 31 24 B2 22 28 58 2D 33 29 28 58 |3)".B1$."(X-3)(X|
00008750: 2D 34 29 22 89 31 36 31 36 30 00 81 90 02 3F 99 |-4)".16160....?.|
00008760: 22 20 4E 4F 2C 20 4E 4F 54 20 22 42 31 24 22 2E |" NO, NOT "B1$".|
00008770: 20 12 28 58 2D 34 29 28 58 2D 33 29 92 20 49 53 | .(X-4)(X-3). IS|
00008780: 22 3A 99 00 AF 90 0C 3F 99 22 20 43 4F 52 52 45 |":.....?." CORRE|
00008790: 43 54 2E 20 28 58 2D 34 29 28 58 2D 33 29 3D 58 |CT. (X-4)(X-3)=X|
000087A0: 91 32 11 2D 33 58 2D 34 58 2B 31 32 20 3D 22 3A |.2.-3X-4X+12 =":|
000087B0: 99 00 DD 90 16 3F 99 22 20 58 91 32 11 2D 37 58 |.....?." X.2.-7X|
000087C0: 2B 31 32 2E 20 4C 45 54 27 53 20 52 45 56 49 45 |+12. LET'S REVIE|
000087D0: 57 20 22 41 31 24 3A 99 3A 89 31 35 32 31 30 00 |W "A1$:.:.15210.|
000087E0: E7 90 20 3F 8D 39 30 30 30 00 13 91 2A 3F 99 22 |.. ?.9000...*?."|
000087F0: 20 9F 45 58 41 4D 50 4C 45 20 33 3A 9A 20 46 41 | .EXAMPLE 3:. FA|
00008800: 43 54 4F 52 49 53 45 20 58 91 32 11 2B 58 9B 2D |CTORISE X.2.+X.-|
00008810: 9A 36 22 3A 99 00 35 91 34 3F 99 22 9F 31 9A 20 |.6":..5.4?.".1. |
00008820: 28 58 20 20 29 28 58 20 20 29 20 53 49 4E 43 45 |(X )(X ) SINCE|
00008830: 20 41 3D 31 22 3A 99 00 45 91 39 3F 81 4C B2 31 | A=1":..E.9?.L.1|
00008840: A4 34 30 30 30 3A 82 00 6E 91 3E 3F 99 22 9F 32 |.4000:..n.>?.".2|
00008850: 9A 20 28 58 9F 2B 9A 20 29 28 58 9B 2D 9A 20 29 |. (X.+. )(X.-. )|
00008860: 20 53 49 4E 43 45 20 43 3D 9B 2D 9A 36 22 3A 99 | SINCE C=.-.6":.|
00008870: 00 7E 91 43 3F 81 4C B2 31 A4 34 30 30 30 3A 82 |.~.C?.L.1.4000:.|
00008880: 00 B7 91 48 3F 99 22 9F 33 9A 20 28 58 9F 2B 33 |...H?.".3. (X.+3|
00008890: 9A 29 28 58 9B 2D 32 9A 29 20 53 49 4E 43 45 20 |.)(X.-2.) SINCE |
000088A0: 9F 28 2B 33 29 9A 2B 9B 28 2D 32 29 9A 3D 9F 2B |.(+3).+.(-2).=.+|
000088B0: 31 9A 20 41 4E 44 22 3A 99 00 CF 91 52 3F 99 A6 |1. AND":....R?..|
000088C0: 31 38 29 22 28 33 29 28 2D 32 29 3D 2D 36 22 3A |18)"(3)(-2)=-6":|
000088D0: 99 00 DF 91 57 3F 81 4C B2 31 A4 34 30 30 30 3A |....W?.L.1.4000:|
000088E0: 82 00 10 92 5C 3F 99 22 20 53 4F 20 28 58 2B 33 |....\?." SO (X+3|
000088F0: 29 28 58 2D 32 29 20 41 52 45 20 54 48 45 20 46 |)(X-2) ARE THE F|
00008900: 41 43 54 4F 52 53 2E 20 4E 4F 57 20 59 4F 55 22 |ACTORS. NOW YOU"|
00008910: 3A 99 00 38 92 66 3F 99 22 20 54 52 59 20 22 41 |:..8.f?." TRY "A|
00008920: 31 24 22 2E 20 46 41 43 54 4F 52 49 53 45 20 58 |1$". FACTORISE X|
00008930: 91 32 11 2B 58 2D 32 22 3A 99 00 5E 92 70 3F 97 |.2.+X-2":..^.p?.|
00008940: 31 39 38 2C 30 3A 85 20 22 20 12 28 D2 D2 D2 29 |198,0:. " .(...)|
00008950: 28 D2 D2 D2 29 22 3B 42 31 24 3A 99 22 92 93 22 |(...)";B1$:.".."|
00008960: 00 8B 92 7A 3F 8B 42 31 24 B2 22 28 58 2B 32 29 |...z?.B1$."(X+2)|
00008970: 28 58 2D 31 29 22 B0 42 31 24 B2 22 28 58 2D 31 |(X-1)".B1$."(X-1|
00008980: 29 28 58 2B 32 29 22 89 31 36 32 39 30 00 B1 92 |)(X+2)".16290...|
00008990: 84 3F 99 22 20 4E 4F 2C 20 4E 4F 54 20 22 42 31 |.?." NO, NOT "B1|
000089A0: 24 22 2C 20 12 28 58 2B 32 29 28 58 2D 31 29 92 |$", .(X+2)(X-1).|
000089B0: 22 3A 99 00 E5 92 8E 3F 99 22 20 49 53 20 43 4F |":.....?." IS CO|
000089C0: 52 52 45 43 54 2E 20 52 45 4D 45 4D 42 45 52 20 |RRECT. REMEMBER |
000089D0: 22 41 31 24 22 2C 20 53 49 4D 50 4C 45 22 3A 99 |"A1$", SIMPLE":.|
000089E0: 3A 89 31 35 32 34 30 00 EF 92 A2 3F 8D 39 30 34 |:.15240....?.904|
000089F0: 30 00 1C 93 AC 3F 99 22 20 4F 4B 20 22 41 31 24 |0....?." OK "A1$|
00008A00: 22 20 57 45 20 57 49 4C 4C 20 48 41 56 45 20 41 |" WE WILL HAVE A|
00008A10: 20 53 48 4F 52 54 20 51 55 49 5A 22 3A 99 00 4B | SHORT QUIZ":..K|
00008A20: 93 B6 3F 99 22 20 4F 4E 20 46 41 43 54 4F 52 49 |..?." ON FACTORI|
00008A30: 53 41 54 49 4F 4E 2E 20 54 48 49 53 20 54 4F 50 |SATION. THIS TOP|
00008A40: 49 43 20 57 49 4C 4C 20 42 45 22 3A 99 00 76 93 |IC WILL BE":..v.|
00008A50: C0 3F 99 22 20 44 45 41 4C 54 20 57 49 54 48 20 |.?." DEALT WITH |
00008A60: 46 55 52 54 48 45 52 20 49 4E 20 50 41 52 54 20 |FURTHER IN PART |
00008A70: 46 4F 55 52 2E 22 3A 99 00 A8 93 CA 3F 99 22 20 |FOUR.":.....?." |
00008A80: 9B 4D 41 4B 45 20 53 55 52 45 20 54 48 41 54 20 |.MAKE SURE THAT |
00008A90: 59 4F 55 20 48 41 56 45 20 50 45 4E 43 49 4C 20 |YOU HAVE PENCIL |
00008AA0: 26 20 50 41 50 45 52 22 3A 99 00 C0 93 D4 3F 99 |& PAPER":.....?.|
00008AB0: 22 20 22 41 31 24 22 9A 2E 11 11 11 11 11 11 11 |" "A1$".........|
00008AC0: 11 22 00 CA 93 DE 3F 8D 39 33 30 30 00 D0 93 E8 |."....?.9300....|
00008AD0: 3F 8E 00 00 94 40 9C 99 22 20 20 20 20 9F 54 48 |?....@.." .TH|
00008AE0: 45 20 54 4F 50 49 43 53 20 46 4F 52 20 50 41 52 |E TOPICS FOR PAR|
00008AF0: 54 20 54 48 52 45 45 20 41 52 45 22 3A 99 3A 99 |T THREE ARE":.:.|
00008B00: 3A 99 00 22 94 4A 9C 99 22 9F 31 20 4F 50 45 52 |:..".J..".1 OPER|
00008B10: 41 54 49 4F 4E 53 20 57 49 54 48 20 53 55 52 44 |ATIONS WITH SURD|
00008B20: 53 22 3A 99 00 49 94 54 9C 99 22 9F 32 20 41 4C |S":..I.T..".2 AL|
00008B30: 47 45 42 52 41 20 49 20 2D 20 53 49 4D 50 4C 49 |GEBRA I - SIMPLI|
00008B40: 46 49 43 41 54 49 4F 4E 22 3A 99 00 70 94 5E 9C |FICATION":..p.^.|
00008B50: 99 22 33 20 20 41 4C 47 45 42 52 41 20 49 49 20 |."3 ALGEBRA II |
00008B60: 2D 20 46 41 43 54 4F 52 49 53 41 54 49 4F 4E 22 |- FACTORISATION"|
00008B70: 3A 99 00 9D 94 68 9C 99 22 9A 20 48 41 56 45 20 |:....h..". HAVE |
00008B80: 59 4F 55 20 41 4C 52 45 41 44 59 20 43 4F 4D 50 |YOU ALREADY COMP|
00008B90: 4C 45 54 45 44 20 41 4E 59 20 4F 46 22 3A 99 00 |LETED ANY OF":..|
00008BA0: C6 94 72 9C 99 22 20 54 48 45 53 45 20 54 4F 50 |..r.." THESE TOP|
00008BB0: 49 43 53 20 22 41 31 24 22 3F 20 41 4E 53 57 45 |ICS "A1$"? ANSWE|
00008BC0: 52 20 59 45 53 22 3A 99 00 EB 94 7C 9C 97 31 39 |R YES":....|..19|
00008BD0: 38 2C 30 3A 85 20 22 20 4F 52 20 4E 4F 2E 20 12 |8,0:. " OR NO. .|
00008BE0: D2 D2 D2 22 3B 42 31 24 3A 99 22 92 22 00 03 95 |...";B1$:."."...|
00008BF0: 86 9C 8B 42 31 24 B2 22 4E 4F 22 A7 99 22 93 22 |...B1$."NO".."."|
00008C00: 3A 89 31 34 30 00 18 95 8B 9C 8B 42 31 24 B2 22 |:.140......B1$."|
00008C10: 59 45 53 22 89 34 30 30 38 30 00 3D 95 8C 9C 99 |YES".40080.=....|
00008C20: 22 20 9B 54 59 50 45 20 49 4E 20 59 45 53 20 4F |" .TYPE IN YES O|
00008C30: 52 20 4E 4F 9A 22 3A 99 3A 89 34 30 30 34 30 00 |R NO.":.:.40040.|
00008C40: 6D 95 90 9C 99 22 20 44 4F 20 59 4F 55 20 57 49 |m...." DO YOU WI|
00008C50: 53 48 20 54 4F 20 53 54 41 52 54 20 57 49 54 48 |SH TO START WITH|
00008C60: 20 54 4F 50 49 43 20 31 20 46 4F 52 22 3A 99 00 | TOPIC 1 FOR":..|
00008C70: 9C 95 9A 9C 85 20 22 20 41 20 52 45 56 49 45 57 |..... " A REVIEW|
00008C80: 3F 20 9B 28 59 45 53 20 4F 52 20 4E 4F 29 9A 20 |? .(YES OR NO). |
00008C90: 12 D2 D2 D2 22 3B 42 32 24 3A 99 22 92 22 00 B5 |....";B2$:."."..|
00008CA0: 95 A4 9C 8B 42 32 24 B2 22 59 45 53 22 A7 99 22 |....B2$."YES".."|
00008CB0: 93 22 3A 89 31 35 30 00 C9 95 A9 9C 8B 42 32 24 |.":.150......B2$|
00008CC0: B2 22 4E 4F 22 89 34 30 31 31 30 00 EE 95 AA 9C |."NO".40110.....|
00008CD0: 99 22 20 9B 54 59 50 45 20 49 4E 20 59 45 53 20 |." .TYPE IN YES |
00008CE0: 4F 52 20 4E 4F 9A 22 3A 99 3A 89 34 30 30 38 30 |OR NO.":.:.40080|
00008CF0: 00 1B 96 AE 9C 99 22 20 44 4F 20 59 4F 55 20 57 |......" DO YOU W|
00008D00: 49 53 48 20 54 4F 20 53 54 41 52 54 20 57 49 54 |ISH TO START WIT|
00008D10: 48 20 54 4F 50 49 43 20 32 3F 22 3A 99 00 4A 96 |H TOPIC 2?":..J.|
00008D20: B8 9C 85 20 22 20 20 20 20 20 20 20 20 20 20 20 |... " |
00008D30: 9B 28 59 45 53 20 4F 52 20 4E 4F 29 9A 20 12 D2 |.(YES OR NO). ..|
00008D40: D2 D2 22 3B 42 33 24 3A 99 22 92 22 00 65 96 C2 |..";B3$:.".".e..|
00008D50: 9C 8B 42 33 24 B2 22 59 45 53 22 A7 99 22 93 22 |..B3$."YES".."."|
00008D60: 3A 89 34 30 32 30 30 00 7F 96 C7 9C 8B 42 33 24 |:.40200......B3$|
00008D70: B2 22 4E 4F 22 A7 99 22 93 22 3A 89 34 30 31 34 |."NO"..".":.4014|
00008D80: 30 00 A4 96 C8 9C 99 22 20 9B 54 59 50 45 20 49 |0......" .TYPE I|
00008D90: 4E 20 59 45 53 20 4F 52 20 4E 4F 9A 22 3A 99 3A |N YES OR NO.":.:|
00008DA0: 89 34 30 31 31 30 00 D5 96 CC 9C 99 22 20 54 48 |.40110......" TH|
00008DB0: 41 54 20 4C 45 41 56 45 53 20 46 41 43 54 4F 52 |AT LEAVES FACTOR|
00008DC0: 49 53 41 54 49 4F 4E 2C 20 42 55 54 20 54 4F 20 |ISATION, BUT TO |
00008DD0: 4D 41 4B 45 22 3A 99 00 0B 97 D6 9C 99 22 20 53 |MAKE":......." S|
00008DE0: 55 52 45 20 54 48 41 54 20 59 4F 55 27 52 45 20 |URE THAT YOU'RE |
00008DF0: 52 45 41 44 59 20 57 45 27 4C 4C 20 53 54 41 52 |READY WE'LL STAR|
00008E00: 54 20 57 49 54 48 11 22 3A 89 34 34 30 00 34 97 |T WITH.":.440.4.|
00008E10: 08 9D 99 22 20 4F 4B 20 22 41 31 24 22 20 4A 55 |..." OK "A1$" JU|
00008E20: 53 54 20 54 4F 20 4D 41 4B 45 20 53 55 52 45 20 |ST TO MAKE SURE |
00008E30: 54 48 41 54 11 22 00 6A 97 12 9D 99 22 20 59 4F |THAT.".j...." YO|
00008E40: 55 20 4B 4E 4F 57 20 54 48 45 20 4D 41 54 45 52 |U KNOW THE MATER|
00008E50: 49 41 4C 20 57 45 27 4C 4C 20 53 54 41 52 54 20 |IAL WE'LL START |
00008E60: 57 49 54 48 22 3A 99 3A 89 31 36 35 00 75 97 22 |WITH":.:.165.u."|
00008E70: F6 81 4C B2 31 A4 37 00 8E 97 2C F6 97 35 33 32 |..L.1.7...,..532|
00008E80: 38 30 2C 31 33 3A 81 54 B2 31 A4 31 30 30 3A 82 |80,13:.T.1.100:.|
00008E90: 00 A8 97 36 F6 97 35 33 32 38 30 2C 35 3A 81 54 |...6..53280,5:.T|
00008EA0: B2 31 A4 31 30 30 3A 82 3A 82 00 B8 97 40 F6 97 |.1.100:.:....@..|
00008EB0: 35 33 32 38 30 2C 31 34 3A 8E 00 D4 97 E0 F6 81 |53280,14:.......|
00008EC0: 54 B2 31 A4 31 30 30 30 3A 82 3A 99 22 93 22 3A |T.1.1000:.:.".":|
00008ED0: 81 4C B2 31 A4 37 00 E5 97 EA F6 99 22 11 11 11 |.L.1.7......"...|
00008EE0: 11 11 11 11 11 11 22 00 02 98 F4 F6 99 A6 39 29 |......".......9)|
00008EF0: 22 1E 50 45 52 46 45 43 54 20 53 43 4F 52 45 20 |".PERFECT SCORE |
00008F00: 22 41 31 24 00 16 98 FE F6 81 54 B2 31 A4 35 30 |"A1$......T.1.50|
00008F10: 30 3A 82 3A 99 22 93 22 00 27 98 08 F7 99 22 11 |0:.:.".".'....".|
00008F20: 11 11 11 11 11 11 11 11 22 00 44 98 12 F7 99 A6 |........".D.....|
00008F30: 39 29 22 9F 50 45 52 46 45 43 54 20 53 43 4F 52 |9)".PERFECT SCOR|
00008F40: 45 20 22 41 31 24 00 60 98 1C F7 81 54 B2 31 A4 |E "A1$.`....T.1.|
00008F50: 35 30 30 3A 82 3A 99 22 93 22 3A 82 3A 99 22 9A |500:.:.".":.:.".|
00008F60: 20 22 00 66 98 26 F7 8E 00 00 00 | ".f.&..... |
.......818,165:.775,168:.G(8).@....788,5
2:.787,64:.792,19:.793,3.J....3000:.".".
14)"...COMPUTER TUTOR....".......7)".BAS
IC ARITHMETIC AND ALGEBRA."...(...15)"PA
RT THREE..".L.-...11)".(C) COPYRIGHT 198
3.."...2...20)".BY.."...<...7)"JOHN C PA
YNTER B.SC.,MAPSS."...F...20)"&.".>.P...
5)"MARY ANN PAYNTER B.A.(HONS) SYD...".}
.Z.." .PLEASE TYPE IN YOUR FIRST NAME FO
R ME..":A1$."LEARNER"...D.. " .RRRRRRR";
A1$:.".."...I.A1$.H(A1$,8).W.N.." .VERY
NICE TO SEE YOU AGAIN "A1$"..."...X.." .
I AM ASSUMING THAT YOU HAVE COMPLETED.".
....." PART TWO!..".&....40000.R...." TH
E FIRST TOPIC FOR PART THREE IS:.".S....
.9)".OPERATIONS WITH SURDS".......9)"...
....................". . ..10000.....X.0
:K.1.V...." .QUIZ ONE - OPERATIONS WITH
SURDS"......". .........................
........".2...." .BE VERY CAREFUL TYPING
IN YOUR ANSWERS.".B...." SINCE ONE ERRO
R STARTS THE QUIZ OVER &."......" TWO ER
RORS MEANS YOU HAVE TO REVIEW."...C.." T
HE SECTION. .YOU MAY USE PENCIL, PAPER."
...H.." AND A CALCULATOR..."...M..A2.10.
....O..K.2.470...P..K.3.760.-.R..".1 (19
82) EXPRESS AS AN INTEGER:..".D.W.Z.0:.1
98,0:. " .N7.... V.N63...... .RR";B1$:.
"..".....C1$."21":.B1$."21"..8090......Z
.0.250......8020.M....".2 (1977) TYPE IN
THE MISSING VALUE:..":.198,0.....Z.0:.
" .N45...... +.N80...... = A.N5.... A
= .RR";B1$:."..".+...C1$."7":.B1$."7"..8
090.8....Z.0.290.B....8020.P."..".3 (197
7) TYPE IN THE MISSING VALUE:.."...'.."
4+.N3...."...,.." FFFFF = B-2.N3...."...
1.." 2+.N3....":.:....6.Z.0:.198,0:. " S
O B= .RR";B1$:.".."...@.C1$."5":.B1$."5"
..8090...J..Z.0.350...T..8020.<.^..".4 (
1981) TYPE IN THE MISSING VALUES:..".I.C
.." 1".Z.H.." FFFFFF = A + B.N13.....
. WHERE A & B ARE"...M.." 4-.N13......":
..H.R.Z.0:.198,0:. " RATIONAL NUMBERS. A
= .R/R";B1$:."."...W.. "
B= .R/R";B2$:."..".".|.C1$."4/3,1/3":
.B1$."4/3".B2$."1/3"..8090./....Z.0.410.
9....8020.Z.....12)".END QUIZ ONE.":.632
00.W...." THE NEXT TOPIC IS:":........6)
".ALGEBRA I - SIMPLIFICATION.".E.....6)"
............................".Q.... 1111
0.....X.0:K.2.......6)".QUIZ TWO - SIMPL
IFICATION.".).B...6)"...................
........".8.G.A2.10:.180.A.L.A2.0.L.V.."
.1 (1982) EXPRESS AS AN INTEGER:..."....
.Z.0:.198,0:. " 8.-2/3.V 4.3/2.= .RR";B1
$:."..".....C1$."2":.B1$."2"..8090.G....
Z.0.510.Q....8020......".2 (1978) FIND T
HE EXACT VALUE (AS A RA-.".4...." TIONAL
NUMBER IN ITS LOWEST TERMS) OF:...".]..
.." A.4.C 2 2 4 4 8 7"...
..." ... WHERE A=(.) ,B=(.) ,C=(.) "....
.." .B.4 3 3 3...".Q
...Z.0:.198,0:. " .R/R";B1$:.".."...&.C1
$."3/8":.B1$."3/8"..8090...0..Z.0.580...
:..8020.8.D..".3 (1972) SIMPLIFY EACH OF
THE FOLLOWING.".G.N.." EXPRESSIONS. NO
NEGATIVE OR ZERO EXP-."...S.." ONENTS SH
OULD APPEAR IN YOUR FINAL AN-.".E.X.." S
WERS AND IT IS GIVEN THAT NEITHER X."...
B.." NOR Y IS ZERO...."...G.." (8X).
-1.".0.L.Z.0:.198,0:. " (A) ..........2.
-6. = .R/R";B1$:.".":.:..O.Q.C1$."8/X":.
B1$."8/X"..8090.\.V..Z.0.650.F....8020..
....:.:." XY.-1.+YX.-1.".H...Z.0:.19
8,0:. " (B) ...............X.2.+Y.2. =
.R/RR";B1$:."..".....C1$."1/XY":.B1$."1/
XY".B1$."1/YX"..8090......Z.0.690......8
020.D....".4 (1973) GIVEN THAT X =.N2...
.+1, SIMPLIFY:.":.:..V...Z.0:.198,0:. "
X - ...1...X. = .RR";B1$:."..".....C1$."
2":.B1$."2".B1$."2/1"..8090......Z.0.710
...A..8020.S.F...12)".END QUIZ TWO.":.63
200...K.." THE NEXT TOPIC IS:."...P...6)
".ALGEBRA II - FACTORISATION.".=.U...6)"
............................".I.Z.. 1350
0.X...X.0:K.3:..6)".QUIZ THREE - FACTORI
SATION.".......6)"......................
......".....A2.10:.180.....A2.0.Q....".1
FACTORISE:.....".....Z.0:.198,0:. " 12X
+6Y .R(RRRR)";B1$:."..".&...C1$."6(2X+Y)
":.B1$."6(2X+Y)"..8090.3....Z.0.810.=. .
.8020.\.*..".":.".2 FACTORISE:....."...4
.Z.0:.198,0:. " 3X.2.+6X .RR(RRR)";B1$:.
"..".A.>.C1$."3X(X+2)":.B1$."3X(X+2)".B1
$."(X+2)3X"..8090.N.H..Z.0.860.X.R..8020
...\..".":.".3 FACTORISE:....."...F.Z.0:
.198,0:. " 9X.2.-Y.2. .(RRRR)(RRRR)";B1$
:."..".E.K.C1$."(3X+Y)(3X-Y)".K.P..B1$.C
1$.B1$."(3X-Y)(3X+Y)"..8090.X.Z..Z.0.910
......8020......".":.".4 FACTORISE:.....
".S...." 9X.2.+12XY+4Y.2. (USE ( )^2 FOR
( ).2.)..".....Z.0:.198,0:. " .(RRRRR)^
R";B1$:."..".....C1$."(3X+2Y)^2":.B1$.C1
$..8090.,....Z.0.970.6....8020.U.J..".":
.".5 FACTORISE:....."...T.Z.0:.198,0:. "
4X.2.-9 .(RRRR)(RRRR)";B1$:."..".B...C1
$."(2X+3)(2X-3)":.B1$.C1$.B1$."(2X-3)(2X
+3)"..8090.P....Z.0.1020.Z....8020......
".":.".6 FACTORISE:.....".,...Z.0:.198,0
:. "X.2.+3X+2 .(RRR)(RRR)";B1$:."..".A..
.C1$."(X+2)(X+1)":.B1$.C1$.B1$."(X+1)(X+
2)"..8090.O....Z.0.1070.Y.$..8020......"
.":.".7 FACTORISE:.....".M.8.Z.0:.198,0:
. " X.2.-8X+15 .(RRR)(RRR)";B1$:.".."...
B.C1$."(X-5)(X-3)":.B1$.C1$.B1$."(X-3)(X
-5)". .8090...L..Z.0.1120...V..8020.:.`.
.".":.".8 FACTORISE:.....".N.J.Z.0:.198,
0:. " X.2.+2X-8 .(RRR)(RRR)";B1$:.".."..
.T.C1$."(X+4)(X-2)":.B1$.C1$.B1$."(X-2)(
X+4)"..8090...~..Z.0.1170......8020.....
..11)"......END QUIZ THREE.":.63200...P.
." .THIS COMPLETES PART THREE.....".:.U.
."IT'S BEEN A REAL PLEASURE WORKING WITH
.".^.Z.."YOU. SEE YOU LATER "A1$"...."..
.....25)".TO EXIT.":.9300:.64738........
.D.."..LOADING TEST - CHECK BYTES:..."..
.X.." ".(0).(.(0).0).65536" BYTES FREE..
.":.2020......"......NOTE: THE 'RUN/STOP
' KEY WILL NOT WORK.".D.B.."WHILE THIS P
ROGRAM IS RUNNING. TO EXIT.".R.L.."BEFOR
E THE END OF THE PROGRAM, SIMPLY."...Q..
"REMOVE THE DISK FROM THE DISK DRIVE AND
.".Q.V.."TURN OFF YOUR COMPUTER. ALSO, Y
OU WILL."......"NOT BE ABLE TO CHANGE TO
LOWER CASE.."......"DON'T WORRY! ALL WI
LL BE BACK TO NORMAL.".I...."WHEN WE FIN
ISH.....".S....9300.Y.....L.T..".":.X.0.
8040...^.." NO, ."C1$". IS RIGHT WE'LL."
.L.C.." START AGAIN. .YOU MAY USE PENCIL
, PAPER.":X.X.1:.200...H.." I'M SORRY BU
T THAT'S TWO ERRORS. WE.".$.R.." WILL HA
VE TO REVIEW THIS SECTION..".1.|..K.1.15
0.>....K.2.420.K....K.3.720.U....9000.E.
..Z.Z.1:.:.:..K.....{.(#Y..(.(0).4)...)#
.Y.0.9007...*#.Y.1.9010...+#.Y.2.9020...
,#.Y.2.9030...-#..Z./#." .SPOT ON "A1$".
..":.63010...0#Y.0:....2#." .THATS RIGHT
"A1$"...":.63010...4#Y.0:..6.<#." .VERY
GOOD "A1$"!..":.63010.@.>#Y.0:..N.F#."
.CORRECT "A1$"! GOOD ON YOU...":.63010.X
.H#Y.0:....P#." .TREMENDOUS! VERY WELL D
ONE "A1$"!..":.63010...R#Y.0:..X.T$.198,
0:..25)".PRESS ANY KEY."...^$.A$:.A$."".
9310...H$.".":A$."":..+ .'." YOU SHOULD
RECALL FROM PART ONE THAT.".B .'." NUMBE
RS SUCH AS .N2....,.N3...., ETC. ARE NOT
.".. $'." RATIONAL. IN GENERAL .THE ROOT
OF A.".. .'." RATIONAL NUMBER WHICH IS
NOT ITSELF.".. 8'." RATIONAL IS CALLED A
.SURD... NOW YOU."..!B'." TELL ME "A1$"
. THE ROOT OF A.".>!L'." RATIONAL NUMBER
WHICH IS NOT ITSELF.".U!V'.198,0:. " RA
TIONAL IS CALLED A ..RRRR";B1$:."..."..!
`'.B1$."SURD".10120..!J'." NO NOT "B1$".
..SURD.. IS CORRECT.."..!T'." REMEMBER
"A1$", .THE ROOT OF A.":.10030..!.'.9000
..".'." IN PERFORMING OPERATIONS INVOLVI
NG.".M".'." SURDS REMEMBER THAT .SURDS O
BEY THE LAWS".~".'." OF ALGEBRA JUST LIK
E RATIONAL NUMBERS..."..".'." FOR EXAMPL
E, JUST LIKE 3.2.V 2.2.= (3V2).2.,":..."
.'." .N3.... V.N2.... =.N3V2........ WHI
CH IS .N6..... CONSIDER":." ".I#D'." .N3
.... V.N12...... =.N3V12.......... =.N36
...... = 6. NOW YOU":." ".Y#N'." TRY ONE
. IN .SIMPLEST TERMS. WHAT IS:":...#X'.1
98,0:. " .N2.... V.N8.... .RR";B1$:.".."
..#.'.B1$."4".10240..#.'." NO, NOT "B1$"
. .4. IS CORRECT.":.:..+$.'." .N2.... V.
N8.... =.N2V8........ =.N16...... = 4. T
RY AGAIN":..6$.'.10130.@$.(.9030.P$.(."
SOMETIMES YOU MIGHT BE ASKED TO SIMP-":.
..$.(." LIFY EXPRESSIONS INVOLVING SURDS
. .FOR":...$.(." EXAMPLE, SIMPLIFY:. .N3
.... +.N12...... .SOLUTION:.":...%((." .
N3.... +.N12...... =.N3.... + .N4V3.....
... =":..R%2(." .N3.... +(.N4.... V.N3..
..) =.N3.... + 2.N3....":...%<(." .WHICH
EQUALS 3.N3...... NOW YOU TRY .(FOR":..
.%F(." A SQUARE ROOT JUST TYPE R IN FRON
T OF":...%P(." THE NUMBER, EG FOR 3.N3..
.. YOU TYPE 3R3).":.:..-&Z(.198,0:. " .S
IMPLIFY:. .N2.... +.N32...... .RRR";B1$:
."..".M&D(.B1$."5R2".B1$."5.N2".10380.~&
N(." NO, NOT "B1$". .YOU SHOULD HAVE TYP
ED.":..E&S(." .5R2.. .N2.... +.N32......
=.N2.... +.N16V2.......... WHICH IS".K&
T(...'X(." .N2.... + 4.N2.... = 5.N2....
. SO YOU TYPE .5R2.":.:.10250..'.(.9040.
H'.(." DIVISION INVOLVING SURDS IS HANDL
ED BY":..Y' (." .RATIONALISING THE DENOM
INATOR.. TO DO":...'.(." THIS YOU MULTIP
LY THE .NUMERATOR & THE":...'.(." DENOMI
NATOR. BY AN APPROPRIATE TERM. FOR"..(.(
." 1 .N2.... .N2....
".0(.(." EXAMPLE: FFF = FFFFFFFF = FFF."
.C(C(." .N2.... .N2.... V.N2.
... 2":...(H(." 1
.N3.... .N3...."..(M(." NOW YOU TRY
: FFF = FFFFFFFF = FFF.".K(O(.198,0..)R(
." .N3.... .N3.... V.N3..
.. .R";B1$:.".."..).(.B1$."3".10510.&
).(.:..Z).(." NO, NOT "B1$". .3. IS CORR
ECT. .N3.... IS":...).(." NOT RATIONAL,
TO .RATIONALISE. THE .DEN-.":...).(."
1 .N3...."..).(
." .OMINATOR. YOU MULTIPLY FFF BY FFF. T
HIS"..*.(." .N3...
. .N3....":..E*.(." .N3....
.N3....".U*.(." EQUALS FFFFFFFF = F
FF SO .3. IS CORRECT"..*.)." .N3.
... V.N3.... .3.":..J*.)." LET'S JUST
GO OVER THIS AGAIN "A1$:...*.).".....":
.9300:.10390..*.). 9000. +.)." THE IDEA
IS TO GET RID OF THE ROOTS IN":..Q+")."
THE DENOMINATOR. SO FOR SOMETHING MORE":
..R+')." .N5.... + 2"..+,).
" COMPLEX LIKE FFFFFFF WE WOULD MULTIPLY
".D+1)." .N5.... - 2":...+6
)." TOP & BOTTOM BY .N5....+2 [SINCE (A-
B)(A+B)"./,@)." EQUALS A.2.-B.2.] SO THE
.NUMERATOR. BECOMES":..F,J)." (.N5....
+ 2).2. & THE .DENOMINATOR. BECOMES":...
,T)." (.N5.... - 2)(.N5.... + 2) = (.N5.
...).2.- 2.2. =":..W,Y)."
.N5.... + 2 (.N5.... + 2).2."..-^)." 5
- 4 = 1. SO FFFFFFF = FFFFFFFFFF =".1-C
)." .N5.... - 2 1":
..D-H)." (.N5....).2.+2.N5.... + 4 = 9 +
2.N5....":..N-R).9300..-|)." NOW YOU TE
LL ME, TO RATIONALISE THE":...-.)."
6"..-.)." DENOMINATOR OF F
FFFFF YOU MULTIPLY THE"....)."
.N3.... - 4":..A..).198,0:. " TOP &
BOTTOM BY .N3.... + .R";B1$:.".".T..).B
1$."4".10670....)." NO, .THE CORRECT ANS
WER IS .4... REMEMBER":."..."....).9300:
.10520....).9000.X..)." OFTEN WHEN YOU R
ATIONALISE THE DENOM-":.../B)." INATORS
& SIMPLIFY EXPRESSIONS INVOLV-":..9/L)."
ING SURDS, YOU ARE LEFT WITH A FRACTION
".J/V)." OR AN INTEGER. THIS SHOWS THAT
THE EX-":.../.)." PRESSION IS RATIONAL.
.EXAMPLE. SHOW THAT"../.)." 6
1"../.)." FFFFFFF . FFFFFF IS RATIONAL.
.SOLUTION."..0.)." .N3.... - 3 2 -.N3
....":..10.)." .(COPY THE PROBLEM "A1$"
& WORK":..`0.*." THROUGH THESE STEPS WIT
H ME PLEASE).":..J0.*.9300..0.*.".1 RATI
ONALISE THE FIRST DENOMINATOR:.":..K0.*.
" 6 6(.N3....+3) 6.N3....+
18"..0.*." FFFFF = FFFFFFFFFFFFFF = FFFF
FFF".)1!*." .N3....-3 (.N3....-3)(.N3.
...+3) 3-9":..@1&*.".2 SIMPLIFY:.":.
.B1+*." 6.N3....+18 6.N3....+18"..10*.
" FFFFFFF = FFFFFFF = -.N3....-3"..15*."
3-9 -6":..R1:*.".3 RATIONALISE
THE NEXT DENOMINATOR:.":...2?*." 1
1(2+.N3....) 2+.N3....".(2D*."
FFFFF = FFFFFFFFFFFFFF = FFFFF".\2I*."
2-.N3.... (2-.N3....)(2+.N3....) 4-
3":..S2N*.".4 SIMPLIFY:.":...2S*." 2+.N3
.... 2+.N3...."..2X*." FFFFF = FFFFF =
2+.N3....".I2]*." 4-3 1":..Y2B*."
..":.9300..2L*.".5 PUT THE TWO TOGETHER:
.":...3Q*." 6 1".@3V*." FFFFF+FFFF
F = -.N3....-3+2+.N3.... = .-1.".^3{*."
.N3....-3 2-.N3....":...3.*." .DO YOU WA
NT TO GO BACK OVER THOSE STEPS"..3.*.198
,0:. " (ANSWER YES OR NO). .RRR";B1$:..S
3.*.B1$."YES".10770..4.*." .GET SOME PAP
ER & A PEN FOR THIS PLEASE":...4.*." "A1
$"..":..G4.*." OK, TRY THIS QUESTION FRO
M THE 1978 HSC".P4.*."
4 1"..4.*." EXAM: BY EXPRESS
ING FFFFF - FFFFFF IN".S4.*."
2+.N5.... 9-4.N5....":...5.*
." ITS SIMPLEST FORM SHOW THAT IT IS A":
..15.*.198,0:. " RATIONAL NUMBER. .RRR";
B1$:."..".^5F*.B1$."-17".B1$."-17/1".B1$
."17/-1".11000..5K*." NO, .-17. IS CORRE
CT. LET'S GO THROUGH":...5P*." THIS STEP
BY STEP "A1$".":...5T*." 4 4(
2-.N5....) 8-4.N5...."..6U*.".1. FF
FFF = FFFFFFFFFFFFFF = FFFFFF".D6V*." 2
+.N5.... (2+.N5....)(2-.N5....) 4-
5":..E6Y*." 8-4.N5.... 8-4.N5...."..6
Z*.".2. FFFFFF = FFFFFF = -8+4.N5...."..
6.*." 4-5 -1":...6.*." 1
1(9+4.N5....) 9+4.N5...."..7
.*.".3. FFFFFF = FFFFFFFFFFFFFFFF = FFFF
FFFF".I7.*." 9-4.N5.... (9-4.N5....)(
9+4.N5....) 81-16(5)":..M7.*." 9+4.N
5.... 9+4.N5.... ". 7.*.".4. FFFFFFFF
= FFFFFF = 9+4.N5.... SO:":...7.*."
81-16(5) 81-80":..I7.*.:.9300..7.*."
4 1 "..8.*.".5. FFFFFF - FFFF
F = -8+4.N5....-(9+4.N5....)".78.*." 2+
.N5.... 9-4.N5....":..N8.*." WHICH EQU
ALS -8+4.N5....-9-4.N5.... = .-17..":...
8.*."...":.9300:.10680..8.*.9040..8.+."
I THINK YOU'VE GOT IT "A1$"!":...8.+." W
E'LL MAKE SURE WITH A SHORT QUIZ. .ALL":
...9.+." THE QUESTIONS ARE QUESTIONS FRO
M PAST":..I9 +." HSC MATHEMATICS EXAMINA
TIONS - 2 UNIT":..{9*+." COURSE.. THE YE
AR OF THE PAPER IS GIVEN":...94+." IN (
) WITH EACH QUESTION. MAKE SURE":..Y9>+
." THAT YOU HAVE MATERIALS (PAPER ETC)":
...9H+." HANDY.":.:.198,0..:R+.".":.9300
..:\+..7:F+." IN ORDER TO SIMPLIFY ALGEB
RAIC EXPRES-":..J:P+." SIONS, WE MUST KN
OW WHAT RULES OR .LAWS.":...:Z+." WE CAN
FOLLOW. THERE ARE THREE .FUNDAM-":...:.
+." ENTAL LAWS. OF ALGEBRA.":..F:.+X.0..
:.+.".1. .COMMUTATIVE. LAW: A+B=B+A & AB
=BA":..';.+." SO X+Y=Y+X IS AN EXAMPLE O
F THE RRRRRR":..P;.+.198,0:. " LAW .RRRR
RRRRRR";B1$:."."..;.+.B1$."COMMUTATIVE".
B1$."COMMUTATIVE LAW".11200..;.+."."..;.
+." NO .COMMUTATIVE. NOT "B1$".":...;.+.
" LOOK AGAIN CAREFULLY "A1$".":.:.11110.
.;.+.9000..<J+.".2. .ASSOCIATIVE. LAW: A
+(B+C)=(A+B)+C &":..K<T+." A(BC)=(AB)C.
SO (XY)Z=X(YZ) IS AN EX-":..S<.+." AMPLE
OF THE RRRRRRRRRRR LAW.":...<.+.198,0:.
" .RRRRRRRRRRR";B1$:.".".L<.+.B1$."ASSO
CIATIVE".B1$."ASSOCIATIVE LAW".11270.U<.
+."."..=.+." NO .ASSOCIATIVE. NOT "B1$".
LETS":..+=.,." LOOK AT THIS AGAIN "A1$"
.":.:.11110.5=.,.9000.C=.,.".3. .DISTRIB
UTIVE. LAW: A(B+C)=AB+AC":...=.,." SO 5(
X+Y)=5X+5Y IS AN EXAMPLE OF THE":...=$,.
" RRRRRRRRRRRR LAW.":..V=.,.198,0:. " .R
RRRRRRRRRRR";B1$:.".."..>8,.B1$."DISTRIB
UTIVE".B1$."DISTRIBUTIVE LAW".11350.2>B,
." NO .DISTRIBUTIVE. NOT "B1$".":..D>L,.
" READ THIS AGAIN CAREFULLY "A1$".":.:.1
1110.N>V,.9000..>`,." THERE ARE ALSO LAW
S FOR DEALING WITH":..K>J,." EXPONENTS,
LOGARITHMS, ETC WHICH WE":...>T,." WILL
LOOK AT LATER. FOR NOW LETS GET":..*?~,.
" SOME PRACTICE. BASICALLY .TO SIMPLIFY"
:..Y?.,." AN ALGEBRAIC EXPRESSION, YOU U
SE THE":...?.,." LAWS APPROPRIATELY, AND
COLLECT LIKE":...?.,.X.1.." .TERMS..":.
:.:.:.11455..?.,." TERMS.. WOULD YOU LIK
E TO GO BACK OVER":...@.,." THE FUNDAMEN
TAL LAWS & .WRITE THEM DOWN?.".@@.,.198,
0:. " (ANSWER YES OR NO) .RRR";B1$:.".."
.Z@.,.B1$."YES".X.1:.11150.I@.,.X.1..930
0..@D,X.0:." .EXAMPLE:. SIMPLIFY 5X-4(2X
-3)":..P@N,." .SOLUTION:. REMOVE THE ( )
A(.B.+.C.)=A.B.+A.C.":...AX,." SO -4(.2
X.-.3.) = -4(.2X.)-(-4)(.3.) = -8X+12.":
..:A.,." 5X-4(2X-3), THEN, EQUALS 5X
-8X+12.":..QA.,." COLLECT LIKE TERMS. 5.
X.-8.X.+12 = -3.X.+12.":...A.,." SINCE A
+B=B+A -3+12X COULD BE WRITTEN":..KA.,."
AS 12X-3. OK "A1$" NOW YOU TRY:":...B.-
.198,0:. " SIMPLIFY 2(X+3)+3(X-2) .RR";B
1$:.".."..B.-.B1$."5X".11570.CB.-." NO,
.5X. IS CORRECT. 2(X+3)+3(X-2) =":..TB.-
." 2X+6 + 3X-6 = 2X+3X+6-6 = 5X+0 = .5X.
.":...B(-." REMEMBER "A1$", TO SIMPLIFY"
:.:.11400..B2-.9000..B<-." THE COMMUTATI
VE LAW HOLDS F0R ANY NUM-":...CF-." BER
OF TERMS, EG A(B+C+D)=AB+AC+AD, SO":..?C
P-." 2(X.2.-4X+3) = 2X.2.-8X+6. IN THIS
CASE":..QCZ-." A=2;B=X.2.;C=-4X & D=3. N
OW YOU TRY ONE":...CD-." .(TO TYPE X.2.
USE ^ FOR 'RAISED TO THE":..NCN-." POWER
'. I.E. FOR X.2. TYPE X^2).":...DX-.198,
0:. " 3(X.2.+2X-4)=.RRRRRRRRR";B1$:.".."
..D.-.B1$."3X^2+6X-12".11700.;D.-." NO,
NOT "B1$" "A1$".":..ID.-." .3X^2+6X-12.
IS THE CORRECT ANSWER.":...D -." 3(X.2.+
2X-4) = 3(X.2.)+3(2X)+3(-4) =":..LD.-."
3X.2.+6X-12 SO YOU TYPE .3X^2+6X-12. LOO
K":...D.-." AT THIS AGAIN "A1$".":.:.115
80..D.-.9040.)E.-." OFTEN, "A1$" WE HAVE
PROBLEMS LIKE":..AEH-." (2X+3)(X-1). SI
NCE .A.B.=.B.A., .(A+B).(C+D).":..~ER-..
25)"= .(C+D).(A+B).":.. E.-..23)"= .(C+D
).A+.(C+D).B.":..CE.-..22)"OR .A.(C+D).+
B.(C+D).":...E.-." SO"," .(A+B).(C+D). =
.A.(C+D).+B.(C+D).":..1F.-." LIKEWISE"
,".(2X+3).(X-1). = .2X.(X-1).+3.(X-1).":
..IF..." = .(2X).(X).+.(2X).(-1).+.(3).(
X).+.(3).(-1).":..OF.....F..." = 2X.2..-
4X+3X-3 = 2X.2..-X-3. NOW YOU TRY:":..HF
...:." .(USE X^2 FOR X.2.).":.:...F...19
8,0:. " (3X-2)(X+1) = .RRRRRRR";B1$:."."
..G"..B1$."3X^2+X-2".11870..G'..".".JG,.
." NO, YOU SHOULD HAVE TYPED .3X^2+X-2."
:..PG1...G6.." .(3X-2).(X+1).=.3X.(X+1)
.-2.(X+1). =":...G;....G@.." 3X.2.+3X-2X
-2 = 3X.2.+X-2 SO .3X^2+X-2. IS":...GE..
..GJ.." CORRECT. LET'S GO BACK A BIT "A1
$".":..!HT.." REMEMBER, IF YOU WANT TO S
IMPLIFY":.:.11400.+H^..9000.]H`..198,0:.
" AND (X+2).2.= .RRRRRRRR";B1$:."..".WH
B..B1$."X^2+4X+4".11888..HD.." NO, NOT "
B1$" .X^2+4X+4. IS RIGHT.":.:..UHF.." (X
+2).2.=(X+2)(X+2)=X(X+2)+2(X+2)=":.:...I
H.." X.2.+2X+2X+2.2.=X.2.+4X+4 SO YOU SH
OULD":..@IJ.." TYPE .X^2+4X+4. IF YOU WA
NT TO SIMPLIFY":.:.11400.JIP..9000.ZIQ..
" BEFORE WE ADD & SUBTRACT EXPRESSIONS,"
:...IR.." "A1$", RECALL THAT -(A+B+C) ME
ANS":..WI|.." -1 TIMES (A+B+C) = (-A)+(-
B)+(-C) THAT":...J..." IS, -A-B-C. SO -(
A-B+C)=-A+B-C. NOW":..;J...198,0:. " ITS
YOUR TURN. -(1+4-3) = .R";B1$:.".".YJ..
.B1$."-1-4+3".. " .CORRECT, .AND THIS EQ
UALS .R";B1$:."."..J...B1$."-2".11960..J
...".".IJ..." NO, .-2. IS CORRECT. -(1+4
-3)= -1(1+4-3)":...J..." WHICH IS (-1)(1
)+(-1)(4)+(-1)(-3) =":../K..." -1-4+3 =
.-2.. OK LET'S TRY THIS AGAIN":.:.11890.
9K...9000.FKB..198,0:. " SO 5X-(4X-2) =
.RRR";B1$:.".".{KL..B1$."X+2".12020..KQ.
."."..KV.." NO, .X+2. IS CORRECT. 5X-(4X
-2)=5X-4X+2":...K..." = .X+2.. WE HAD BE
TTER REVIEW "A1$".":.:.11860..K...9000.'
L..." NOW TRY ONE SLIGHTLY MORE COMPLICA
TED.":..LL./." SIMPLIFY: 3X-2Y+7-(X+2Y-3
)":..PL./.198,0:. " .RRRRRRRR";B1$:.".."
..L./.B1$."2X-4Y+10".12080..L!/." .2X-4Y
+10. IS RIGHT, NOT "B1$:...L&/." 3X-2Y+7
-(X+2Y-3) = .3X.-.2Y.+7-.X.-.2Y.-3 =":..
)M+/." .3X.-.X.-.2Y.-.2Y.+7+3 = .2X-4Y+1
0.. TO SIMPLIFY":.:.11400.3M0/.9000.^M:/
." AS I MENTIONED, "A1$", THERE ARE":...
MD/." LAWS FOR DEALING WITH EXPONENTS(PO
WERS)".CMN/." THESE ARE: .(WRITE THEM DO
WN AS YOU GO).":.:...NX/.".1. A.X.A.Y.=
A.X+Y. SO X.2.X.3.= X.5. (TYPED AS .X^5.
)":..=NB/.198,0:. " NOW YOU TRY ONE, X.3
.X.4.= .R^R";B1$:.".".RNL/.B1$."X^7".121
70.[NQ/."."..NV/." NO, .X^7. IS CORRECT.
X.3.X.4.= X.3+4.= X.7.":..GN./." SO YOU
SHOULD TYPE .X^7.. TRY AGAIN":.:.12090.
QN./.9000..O./.".2. (AB).X.= A.X.B.X. SO
(2X).3.= 2.3.X.3.= 8X.3. SO":..;O./." Y
OU TYPE .8X^3.. NOW YOU TRY ONE:":..DO./
.198,0:. " (4X).2.= .RRR^R";B1$:."."..O.
/.B1$."4^2X^2". . " .CORRECT!. BUT 4.2.X
.2.= .RRR^R";B1$:."."..O./.B1$."16X^2".1
2240.EO./."."..O./." NO, .16X^2. IS CORR
ECT, NOT "B1$".":..)PA/." (4X).2.= 4.2.X
.2.= 16X.2. SO YOU SHOULD TYPE":..`PF/."
.16X^2.. LET'S START THIS PART AGAIN.":
.:.12090.JPP/.9000..PZ/.".3. (A.X.).Y.=
A.XY. SO (X.2.).3.= X.6., SO YOU TYPE":.
..P./.198,0:. " .X^6.. NOW YOU TRY, (X.4
.).2.= .R^R";B1$:."."..P./.B1$."X^8".123
00..Q./.".".8Q./." NO, NOT "B1$" .X^8. I
S CORRECT. (X.4.).2.=":..RQ.0." X.8. SO
YOU SHOULD TYPE .X^8.. THERE ARE":.:.121
00.|Q.0.9000..Q.0.198,0:. ".4. A.0.= 1,
SO X.0.= 1 & (X.2.).0.= .R";B1$:.".."..Q
.0.B1$."X^0". . " .THAT'S RIGHT., BUT X.
0.= .R";B1$:."."..R 0.B1$."1".12350.FR*0
." NO .1. IS CORRECT. (X.2.).0.= X.(2)(0
).= X.0.= 1":..TR40." LET'S REVIEW THE L
AWS "A1$".":.:.12110.~R>0.9000..RH0.".5.
IF A IS NOT 0, A.-X.= 1/A.X. SO 5.-2.=
1/5.2.":...RR0.198,0:. " = 1/25 & 2.-3.=
.R/R";B1$:."."."SW0.B1$."1/2^3". . " .C
ORRECT!. & 1/2.3. = .R/R";B1$:.".".NS\0.
B1$."1/8".B1$.".125".B1$."0.125".12400..
SA0.".":." NO, NOT "B1$" .1/8. IS RIGHT.
2.-3.= 1/2.3.":...SC0." WHICH EQUALS .1
/8.":..WSF0." "A1$", WE HAD BETTER REVIE
W THE":.:.12100..SP0.9040..TZ0.".6. IF A
IS NOT 0, A.X./A.Y.= A.X-Y. SO X.3./X.2
.=":..ST.0.198,0:. " X.3-2.= X, & X.5./X
.3.= .R^R";B1$:."."..T.0.B1$."X^5-3". .
" YOU MEAN X^(5-3) BUT X.5-3.= .R/R";B1$
:.".".OT.0.B1$."X^(5-3)". . " .YES. AND
X.5-3. = .R^R";B1$:."."..T.0.B1$."X^2".1
2460..T.0.".".!U.0." NO, NOT "B1$". .X^2
. IS RIGHT. X.5./X.3.=":..RU.0." X.5-3.=
X.2. SO YOU SHOULD TYPE .X^2..":...U.0.
" "A1$", LETS LOOK AGAIN AT THE":.:.1210
0..U.0.9000.OU.0.".7. A.1/Y.=.Y...NA....
(YTH ROOT OF A) SO A.1/2. =.NA.....":..
ZU.0.198,0..V.0. " THUS 25.1/2.=.N25....
.. = .5. & 36.1/2.= .R";B1$:."..".,VJ0.B
1$."6".12520.^VT0." NO, NOT "B1$". .6. I
S CORRECT. 36.1/2.=":...V.0." .N36......
= .6.. WE HAD BETTER REVIEW THE":.:.121
00..V.0.9000.LV.0." NOW, "A1$" IN THE AB
OVE LAWS,":...V.0." A & B CAN REFER TO .
ALGEBRAIC EXPRES-":..0W.1." SIONS.. SO (
X+3).2.V(X+3).3.=(X+3).2+3. =":..CW.1."
(X+3).5. OK, LETS LOOK AT SOME EXAMPLES.
":...W.1.:." .SIMPLIFY:. .N25X.2......N.
.....":.:..PW$1.:." .SOLUTION:. .N25X.2.
.....N......=(25X.2.).1/2.=":.:...X.1."
(25).1/2.(X.2.).1/2.= .5X.. NOW YOU TRY
ONE:":.:.:..HX81.198,0:. " .N49X.2.Y.2..
......N........= .RRR";B1$:."..".{XB1.B1
$."7XY".B1$."7YX".B1$."XY7".B1$."YX7".12
650.BXL1.:." NOT "B1$". .7XY. IS CORRECT
..N49X.2.Y.2........N........":.:...YV1.
" = (49X.2.Y.2.).1/2.=(49).1/2.(X.2.).1/
2.(Y.2.).1/2.":..3Y`1." = .7XY.. WE HAD
BETTER REVIEW THE":.:.12100.=YJ1.9040.KY
T1." .ATTENTION TO PLACEMENT OF GROUPING
":.. Y~1." SYMBOLS (),[],.N...,ETC. IS V
ERY IMPORT-":.:..XY.1." ANT!. CONSIDER (
4X)(2X).2. VS [(4X)(2X)].2.":.:...Z.1."
(4X)(2X).2.=(4X)(2.2.X.2.)=(4X)(4X.2.)=1
6X.3. SO":.:..@Z.1." YOU WOULD TYPE .16X
^3.. .BUT:.":.:..}Z.1." [(4X)(2X)].2.=(8
X.2.).2.=(8).2.(X.2.).2.=64X.4. SO":...Z
.1." YOU WOULD TYPE .64X^4.. NOW YOU TRY
ONE:":.:...Z.1.198,0:. " (2Y)
(3Y).2.= .RRR^R";B1$:.".":...[D1.B1$."18
Y^3".12770.6[I1.B1$."18X^3".." .Y. NOT .
X. TRY AGAIN":.:.12730.H[N1.".":." NO, N
OT "B1$". .18Y^3. IS RIGHT.":.:...[S1."
(2Y)(3Y).2.=(2Y)(3.2.Y.2.)=(2Y)(9Y.2.)=1
8Y.3. SO":...[X1." YOU SHOULD TYPE .18Y^
3.. LET'S REVIEW THE":.12100..\.1.198,0:
. " .RIGHT .& [(2Y)(3Y)].2.= .RRR^R";B1$
:."..".J\.1.B1$."36X^4".." .Y. NOT .X. T
RY AGAIN":.:.12730.A\.1.B1$."36Y^4".1282
0..\.1." NO, NOT "B1$". .36Y^4. IS CORRE
CT.":.:..O\.2." [(2Y)(3Y)].2.=[6Y.2.].2.
=6.2.(Y.2.).2.=36Y.4. SO YOU":...].2." S
HOULD TYPE .36Y^4. LET'S GO OVER THE":.:
.12100..].2.9000.:].2." ."A1$", YOU DO H
AVE PAPER & PEN":..J](2." &/OR PENCIL DO
N'T YOU? (ANSWER YES OR":...]22.198,0:.
" NO). .RRR";B1$:.".."..]<2.B1$."YES".12
880.S]A2." WELL YOU HAD BETTER GO GET TH
EM. I'LL":...^F2." WAIT HERE. WHEN YOU C
OME BACK JUST ":...^K2.9300.<^M2." THAT'
S BETTER "A1$" YOU WILL BE":.:.12890.E^P
2." GOOD "A1$" BECAUSE YOU WILL BE":...^
Z2." NEEDING THESE MORE & MORE AS WE GO
ON.":..E^D2." OFTEN WE MUST EVALUATE AN
EXPRESSION":...^N2." GIVEN CERTAIN VALUE
S FOR THE VARIABLES":..'_X2." (X,Y,T,ETC
.) TO DO THIS THE FIRST STEP":..W_.2." I
S TO .SIMPLIFY. THE EXPRESSION, THEN":..
._.2." .'PLUG IN THE VALUES'. AND SIMPLI
FY FUR-":..._.2." THER. .EXAMPLE:. FIND
THE VALUE OF:":.:..._ 2." U.2.(U.2.+2)-(
2T+U.2.) WHEN U=2.N2.... & T=6":.."`.2."
.(WRITE DOWN THE QUESTION PLEASE, THEN"
:..B`.2." PRESS ANY KEY)..":.9300.G`.2.
" .SOLUTION: 1. SIMPLIFY..":.:...`H2." U
.2.(U.2.+2)-(2T+U.2.)=U.4.+2U.2.-2T-U.2.
=":.:..Z`R2." U.4.+U.2.-2T .2. SUBSTIT
UTE. 2.N2.... FOR U &":.:...A.2." 6 FOR
T GIVING: (2.N2....).4.+(2.N2....).2.-2(
6) =":.:..ZA.2." 2.4..N2...4.+2.2..N2...
2.-12 = 16(2).4/2.+4(2).2/2.-12":...A.2.
" = 16(4)+4(2)-12 = 64+8-12 = .60.. NOW"
:...A.2." IT'S YOUR TURN "A1$". EVALUATE
: ":.:...A.3." U.2.(1-U.2.)+(2T-U.2.) WH
EN U=3.N2.... & T=200.":...B.3.198,0:. "
.RR";B1$:."..".#B.3.B1$."76".13130.BB.3
.X.0.. " SORRY THAT'S STILL WRONG. .REVI
EW:.":.:X.0:.11110..B"3." NO NOT "B1$".
.76. IS CORRECT:":..KB'3." .1. U.2.(1-U.
2.)+(2T-U.2.)=U.2.-U.4.+2T-U.2.=-U.4.+2T
":...C,3." OR 2T-U.4. .2. SUBSTITUTE 3.N
2.... FOR U & 200":..CC13." FOR T. 2T-U.
4.=2(200)-(3.N2....).4.=400-3.4..N2...4.
":..WC63." =400-81(2).2. = 400-81(4) = 4
00-324=.76..":..C;3X.1..C@3." REMEMBER
"A1$", THE FIRST STEP":.:.12930..CJ3X.0:
.9040.HCT3.11010.NC^3...C.4." A NUMBER X
IS A .FACTOR. OF A NUMBER Y":..0DF4." I
F X .DIVIDES EXACTLY. INTO Y. NOW YOU":.
.`DP4." TELL ME, IF X DIVIDES EXACTLY IN
TO Y,":...DZ4.198,0:. " THEN X IS A RRRR
R OF Y. .RRRRR";B1$:."."..D.4.B1$."FACTO
R".13560..D.4." NO, .FACTOR. IS CORRECT.
"A1$",":.:.13500..D.4.9000..E.5." SO 4
IS A FACTOR OF 12 SINCE 4 DIVIDES":..JE.
5." EXACTLY INTO 12 (12/4 = 3). ANOTHER"
:..ZE.5." WAY TO SAY THIS IS THAT A NUMB
ER X IS":...E 5." A FACTOR OF A NUMBER Y
, IF Y IS A ":..YE*5." .MULTIPLE. OF X.
SO IF X IS A FACTOR OF":...F45." Y, THEN
Y IS A RRRRRRRR OF X.":..%F>5.198,0:. "
.RRRRRRRR";B1$:."..".?FH5.B1$."MULTIPLE
".13670.LFR5." NO NOT "B1$". .MULTIPLE.
IS RIGHT.":.. F\5." REMEMBER "A1$", THAT
A NUMBER X IS":.:.13600..FF5.9000..FP5.
" SO 3 & 4 ARE .FACTORS. OF 12 SINCE 3V4
=12"..GZ5." 1 IS ALSO A FACTOR OF 12 SIN
CE 1V12=12":..<G.5." IS 12 A FACTOR OF 1
2? (ANSWER YES OR":..^G.5.198,0:. " N0)
.RRR";B1$:.".".SG.5.B1$."YES".13750..G.5
." THAT'S NOT RIGHT. 12 .IS. A FACTOR OF
12":..UG.5." SINCE 12V1=12. LET'S GO TH
ROUGH THIS":...G.5." AGAIN "A1$".":.:.13
500..G.5.9000.+H.5." IF A NUMBER, LIKE 7
, HAS NO FACTORS":.._HJ5." .OTHER THAN I
TSELF OR ONE. IT IS A .PRIME":...HT5." .
NUMBER.. NOW YOU TELL ME, IF A NUMBER":.
.AH.5." HAS NO FACTORS OTHER THAN ITSELF
& ONE":...H.5.198,0:. " IT IS A .RRRR R
RRRR";B1$:.".."..I.5.B1$."PRIME NUMBER".
B1$."PRIMENUMBER".13840.II.5." NO NOT "B
1$". .PRIME NUMBER. IS":..}I.6." CORRECT
. LOOK AT THIS AGAIN "A1$".":.:.13760..I
.6.9000..I.6." SO 7 IS A PRIME NUMBER. I
S 3 A PRIME":...I$6.198,0:. " NUMBER (YE
S OR NO) .RRR";B1$:."."..I.6.B1$."YES".1
3900.,J86." WRONG, .YES. IS RIGHT. 3 .IS
. A PRIME":..[JB6." NUMBER. 3 HAS .NO FA
CTORS OTHER THAN":...JG6." ITSELF AND ON
E.. REMEMBER "A1$".":.:.13760..JL6. 9000
.IJV6.198,0:. " IS 6 A PRIME NUMBER .RR"
;B1$:."."..J`6.B1$."NO".13950..KJ6." WRO
NG, .NO. IS CORRECT. 6 IS .NOT. A PRIME"
:..AKT6." NUMBER. IT .DOES. HAVE FACTORS
OTHER":..SKY6." THAN ITSELF OR ONE. REM
EMBER "A1$:.:.13500.}K~6.9000..K.6." WHA
T IS .ONE. FACTOR OF 6 OTHER THAN":..PK.
6.198,0:. " 6 AND 1 .R";B1$:."."..L.6.B1
$."2".B1$."3".B1$."TWO".B1$."THREE".1401
0.8L.6.B1$."1".B1$."6".." .OTHER THAN 6
OR 1!.":.:.13960.NL.6." "B1$" IS .NOT. A
FACTOR OF 6. .1. OR .3. IS":...L.6." CO
RRECT. "A1$", RECALL THAT":.:.13500..L.6
.9000.WLD6." AND .ANOTHER. FACTOR OTHER
THAN "B1$",6":...LN6.198,0:. " OR 1 IS .
R";B2$:.".."..MX6.B1$."2".B2$."3".14080.
2M.6.B1$."3".B2$."2".14080.EM.6." NO .2.
& .3. ARE THE FACTORS SINCE 2V3=6":...M
.6." "B1$"V"B2$" DOES NOT EQUAL 6.":.:.1
3500..M.7.9040.PM.7." IN GENERAL IF XY=Z
, X & Y ARE .FACTORS.":...N.7." OF Z. CO
NSIDER THE .DISTRIBUTIVE LAW.":../N.7."
FROM THE LAST SECTION. A(B+C)=AB+AC.":..
BN(7." A IS A .COMMON FACTOR. OF THE TER
MS AB &":...N27." AC. SO TO .FACTORISE.
AB+AC WE APPLY THE":..GN<7." .DISTRIBUTI
VE LAW IN REVERSE.. THAT IS:":...NF7." A
B+AC=A(B+C). NOW YOU TRY. FACTORISE":..
OP7.198,0:. " 2X+2Y = .R(R+R)";B1$:.".."
.EOZ7.B1$."2(X+Y)".B1$."2[X+Y]".14200.QO
D7." NO NOT "B1$" .2(X+Y). IS CORRECT.":
.. ON7." LOOK AT THIS AGAIN PLEASE "A1$:
.:.14090..OX7.9000.ZO.7." TO .FACTORISE.
AN EXPRESSION YOU MUST":...P.7." FIND T
HE .HIGHEST COMMON FACTOR.. FOR":..<P.7.
" EXAMPLE 6X+3Y+12Z=3(2X+Y+4Z) .3. IS TH
E":..JP 7." HIGHEST COMMON FACTOR. WHAT
IS THE ":...P.7.198,0:. " HIGHEST COMMON
FACTOR OF4,8 & 16 .R";B1$:."."..P.7.B1$
."4".14290..P.7." NO, .4. IS CORRECT. .4
.V1=4,.4.V2=8,.4.V4=16":..#QH7." SO 4,8
& 16 ARE .ALL MULTIPLES. OF .4..":..RQM7
." REMEMBER "A1$", A NUMBER X IS":.:.136
00.\QR7.9000..Q.7." SO TO .FACTORISE. 4X
+8Y+16Z YOU WRITE":...Q.7.198,0:. " .R(R
RRRRRR)";B1$:."..".NQ.7.B1$."4(X+2Y+4Z)"
.14350..Q.7." NO, NOT "B1$" .4(X+2Y+4Z).
IS":..&R.8." RIGHT. REMEMBER "A1$" IN O
RDER":.:.14210.0R.8.9000.`R.8." THE HIGH
EST COMMON FACTOR IS NOT ALWAYS"..R"8."
JUST A NUMERICAL TERM "A1$". IT":...R,8.
" CAN INCLUDE A VARIABLE, FOR EXAMPLE:":
...R68." 3X IS THE HIGHEST COMMON FACTOR
OF ":...S@8." 3X.2.-6X. SO TO .FACTORIS
E. 3X.2.-6X YOU":..PSJ8." WRITE 3X(X-2)
SINCE 3X.2.-6X=.3X.(X)-.3X.(2)="..ST8."
.3X.(X-2). NOW YOU TRY "A1$" FACTORISE":
...S^8.198,0:. " 4X.2.+12X= .RR(RRR)";B1
$:."..".HSH8.B1$."4X(X+3)".14470..SR8."
NO "B1$" IS NOT CORRECT. THE":..)T|8." C
ORRECT ANSWER IS .4X(X+3).. REMEMBER TO"
:.:.14210.3T.8.9040.GT.8." YOU MAY RECAL
L THAT (A+B)(A-B) = A.2.- B.2."..T.8." T
HIS IS DERIVED USING THE DISTRIBUTIVE":.
.JT.8." LAW: .(A+B).(A-B). = .A.(A-B).+B
.(A-B).":...T.8..17)"= .A.A-.A.B.+B.A-.B
.B.":...U.8..17)"= A.2.-.A.B.+.A.B.-B.2.
":..-UB8..17)"= A.2.- B.2.":..\UL8." SO
(A+B) & (A-B) ARE .FACTORS. OF ":.:...UV
8." A.2.- B.2.. SO TO .FACTORISE. A.2.-
B.2. YOU":...U.8.198,0:. " WRITE .(RRR)(
RRR)";B1$:.".."..U.8.B1$."(A+B)(A-B)".B1
$."(A-B)(A+B)".14610..V.8." NO NOT "B1$"
.(A+B)(A-B). IS":..FV.8." CORRECT. (A+B
)(A-B)=A.2.- B.2., SO (A+B)":..{V.9." &
(A-B) ARE .FACTORS. OF A.2.- B.2.":.:.14
090..V.9.9000..V.9." NOW CONSIDER: 49X.2
.-1":..EV&9.:.,"= 7.2.X.2.- 1.2.":.:...V
09.,"= (7X).2.- 1.2. SINCE (AB).2.=A.2.B
.2.":...W:9.,"= .(7X+1)(7X-1).":..?WD9."
NOW YOU TRY ONE "A1$", FACTORISE:":.:..
UWN9.198,0:. " 25X.2.- 36Y.2. .(RRRR)(RR
R)";B1$:.".."..WX9.B1$."(5X+6Y)(5X-6Y)".
B1$."(5X-6Y)(5X+6Y)".14710.RWB9." NO NOT
"B1$" .(5X+6Y)(5X-6Y).":...XL9." IS RIG
HT. 25X.2.- 36Y.2.= 5.2.X.2.-6.2.Y.2. ="
:..@XQ9." (5X).2.-(6Y).2.=.(5X+6Y)(5X-6Y
). "A1$:.:.14480.JXV9.9000.YX.9." YOU MI
GHT ALSO RECALL THAT (A+B).2.=":...X.9."
A.2.+ 2AB+ B.2.. AGAIN THIS IS DERIVED"
:...X.9." USING THE DISTRIBUTIVE LAW: .(
A+B).(A+B).":.:..%Y.9." =.A.(A+B).+B.(A+
B).= A.2.+.A.B.+.B.A.+B.2.=A.2.+2AB+B.2.
":.:..ZY.9." SO TO .FACTORISE. A.2.+2AB+
B.2. YOU HAVE":.:...YF9." (A+B)(A+B)=(A+
B).2. SO YOU TYPE .(A+B)^2.":...YP9." NO
W YOU TRY "A1$", FACTORISE:":.:...YZ9.19
8,0:. " 4X.2.+4XY+Y.2. .(RRRR)^R";B1$:."
.."..Z.9.B1$."(2X+Y)^2".14860.3Z.9." NO
NOT "B1$" .(2X+Y)^2. IS RIGHT.":.:..MZ.9
." (2X+Y).2.=(2X).2.+2(2X)(Y)+Y.2.= 4X.2
.+4XY+Y.2.":...Z.:." TRY AGAIN "A1$". RE
MEMBER (A+B).2.=":.:.14730..Z.:.9000..Z.
:." SIMILARLY (A.-.B).2.=A.2..-.2AB+B.2.
. SO TO FACT-":...{ :." TORISE X.2..-.2X
Y+Y.2. YOU WOULD TYPE:":2.+....2XY+Y.2.
IS CALLED A":..N|P:." .PERFECT SQUARE. S
INCE IT EQUALS (X+....Y)..2..":...|Z:."
SO X.2.+2XY+Y.2. IS A .RRRRRRR RRRRRR":.
..|.:.198,0:. " .";B1$:.".."..|.:.B1$."P
ERFECT SQUARE".B1$."PERFECTSQUARE".15010
."}.:." NO, .PERFECT SQUARE. IS CORRECT"
A1$:.:.14950.,}.:.9000.\}.:." NOT ALL TE
RMS, HOWEVER, ARE PERFECT":.:...}.:." SQ
UARES. CONSIDER 2X.2.+X-3. THIS IS NOT":
.:..I}.:." IN THE FORM A.2.+....2AB+B.2.
& SO IS .NOT. A":...}J:." PERFECT SQUAR
E. A TERM LIKE THIS IS ":..)~T:." CALLED
A .TRINOMIAL. BECAUSE IT HAS ":.:..T~.:
." THREE TERMS. SO "A1$", 2X.2.+X-3":..}
~.:.198,0:. " IS A .RRRRRRRRR";B1$:.".".
.~.:.B1$."TRINOMIAL".15110.N~.:." NO .TR
INOMIAL. IS CORRECT. 2X.2.+X-3":.:.15060
.X~.;.9000...;." IF A TERM IS OF THE FO
RM AX.2.+BX+C IT":..;.;." IS CALLED A .
QUADRATIC TRINOMIAL. SINCE":..K$;." X I
S RAISED TO THE SECOND POWER. SO":.:...
.;." "A1$", AX.2.+BX+C IS A .RRRRRRRRR":
...8;.198,0:. " .RRRRRRRRR";B1$:.".."..
B;.B1$."QUADRATIC TRINOMIAL".B1$."QUADR
ATICTRINOMIAL".15200...L;." NO "B1$" IS
INCORRECT":..M.V;." .QUADRATIC TRINOMIAL
. IS CORRECT.":.:.15120.W.`;.9000...J;."
QUADRATIC TRINOMIALS CAN BE FACTORISED"
:....T;." USING THE QUADRATIC FORMULA (S
EE PART":....~;." FIVE "A1$") HOWEVER VE
RY .SIMPLE.":.....;." QUADRATIC TRINOMIA
LS CAN BE FACTORISED":..E..;." BY INSPEC
TION (APPLYING THE DISTRIBU-":..T..;." T
IVE LAW IN REVERSE). FOR EXAMPLE:":.:...
..;." X.2.+3X+2 = .(X+2)(X+1). SINCE (X+
2)(X+1)=":.:.....;." X.2.+X+2X+2=X.2.+3X
+2. SO THE .FACTORS. OF":.....;.198,0:.
" X.2.+3X+2 ARE .(RRR)(RRR)";B1$:."..".A
.D;.B1$."(X+2)(X+1)".B1$."(X+1)(X+2)".15
325.J.N;." NO, NOT "B1$". .(X+2)(X+1). I
S":....X;." CORRECT. WE HAD BETTER REVIE
W "A1$:.:.14480....;.9040.X..;." THE FOL
LOWING HINTS WILL HELP IN FACT-":.....;.
" ORISING QUADRATIC TRINOMIALS BY IN-":.
.6..;." SPECTION. .WRITE THESE DOWN AS W
E GO.":..`..<." .CONSIDER AX.2.+BX+C WHE
N A=1.:":.....<.".1. IF A=1, THE FIRST T
ERM IN .BOTH. FACTORS".C..<." IS .X.. (X
+P)(X+Q)=1(X).2.+(P+Q)X+PQ":.....<."
=X.2.+(P+Q)X+PQ. SO TO":..&
.(<." FACTORISE X.2.+5X+6 THE .FIRST TER
M. IN":..U.2<.198,0:. " .BOTH. FACTORS I
S .R";B1$:."..".H.<<.B1$."X".15450...F<.
" NO, NOT "B1$" .X. IS CORRECT. IF A=1":
..G.P<." THEN AX.2.=X.2.. TRY AGAIN "A1$
:.:.15330.Q.Z<.9000...D<.".2. IF B .&. C
ARE POSITIVE THEN THE SIGNS":..,.N<." I
N THE FACTORS ARE BOTH .+..":..I.X<." (X
.+.P)(X.+.Q)=X.2..+.(P+Q)X.+.PQ [A=1;B=.
+.(P+Q);":.....<." C=.+.PQ] SO TO FACTOR
ISE X.2..+.5X.+.6 THE":..T..<.198,0:. "
SIGNS IN BOTH FACTORS ARE .R";B1$:."."..
..<.B1$."+".15550....<.".".&. <." NO NOT
"B1$", .+. IS CORRECT (X.+.P)(X.+.Q)":.
.S..<." =(X)(X).+.(X)(Q).+.(X)(P).+.(P)(
Q)":.....<." =X.2..+.(Q+P)X.+.PQ. LET'S
REVIEW:":.:.15210....<.9000.G.H<.".3. IF
.B IS NEGATIVE. & .C IS POSITIVE. THE":
....R<." SIGNS IN THE FACTORS ARE .BOTH.
.-.":..2..<." (X.-.P)(X.-.Q)=X.2..-.(P+
Q)X.+.PQ [A=1;B=.-.(P+Q);":..G..<." C=.+
.PQ] SO TO FACTORISE X.2..-.5X.+.6 THE":
.....<.198,0:. " SIGNS IN BOTH FACTORS A
RE .R";B1$:.".."....<.B1$."-".15640....=
." NO, THEY ARE BOTH .-.. (X.-.P)(X.-.Q)
=":.....=." (X)(X).-.QX.-.PX.+.PQ = X.2
..-.(Q+P)X.+.PQ. LET'S":..K..=." START A
GAIN ON THIS "A1$".":.:.15210.U..=.9000.
.."=.".4. IF .C. IS .NEGATIVE. THE SIGNS
IN THE":....,=." FACTORS ARE .DIFFERENT
. (X.+.P)(X.-.Q) =":....6=." X.2.+(P-Q)X
.-.PQ [A=1;B=(P-Q);C=.-.PQ] SO TO":..".@
=." FACTORISE X.2.+X.-.6 THE SIGNS IN TH
E":..Q.J=.198,0:." FACTORS ARE .RRRRRRRR
R";B1$:.".".L.T=.B1$."DIFFERENT".15730..
.^=." NO, THE SIGNS ARE .DIFFERENT.. (X.
+.P)(X.-.Q)"...H=." =(X)(X)-QX+PX.-.PQ =
X.2.+(P-Q).-.PQ .REVIEW:.":.:.15210...R
=.9040...|=.".5. IF A=1, THE SECOND TERM
S OF THE FAC-":..H..=." TORS HAVE A SUM=
B & A PRODUCT=C":..X..=." (IN AX.2.+BX+C
) I.E. (X+.P.)(X+.Q.) =":.....=." X.2.+.
(P+Q).X+.PQ. SO "A1$" CON-":..Y..=." SID
ERING X.2.+.5.X+.6., THE SECOND TERMS OF
":.....=.198,0:." THE FACTORS HAVE A SUM
OF .R";B1$:.".".5..=.B1$."5".B1$."2+3".
B1$."3+2".15840.C.B=.".":." NO, NOT "B1$
". .5. IS CORRECT.":....L=." (X+3)(X+2)=
X.2.+.(2+3).X+6. LET'S REVIEW.":.:.15210
....=.9000....=.198,0:. " AND A
PRODUCT OF .R";B1$:.".."....=.B1$."6".1
5900.%..=." NO NOT "B1$". .6. IS CORRECT
. (X+3)(X+2)":..`..>." =X.2.+5X+.(2)(3).
, LET'S REVIEW THIS PART":.:.15210.J..>.
9000...&>.".6. .WRITE DOWN THE FACTORS &
MULTIPLY":..I.0>." THEM OUT TO CHECK!.
OK, LETS LOOK AT":....:>." AN .EXAMPLE:.
FACTORISE X.2.+9X+20":....?>.L.1.4000:.
...D>." .SOLUTION:.":..>.N>.".1. (X )(X
) SINCE A=1":..N.S>.L.1.4000:..}.X>.".
2. (X+ )(X+ ) SINCE B=.+.9 & C=.+.20":..
..]>.L.1.4000:....B>.".3. (X+5)(X+4) SIN
CE 4+5=9 & (4)(5)=20":..M.G>.L.1.4000:..
..L>." NOW YOU TRY: FACTORISE X.2.+7X+12
":....V>.198,0:. " .(RRR)(RRR)";B1$:."..
".L..>.B1$."(X+4)(X+3)".B1$."(X+3)(X+4)"
.16040.Y..>." NO NOT "B1$" .(X+4)(X+3).
IS RIGHT":.....>." (X+4)(X+3)=X.2.+3X+4X
+12 = X.2.+7X+12":.....>." WE HAD BETTER
REVIEW THIS "A1$".":.:.15210....>.9040.
...>." .EXAMPLE 2:. FACTORISE X.2.-5X+6"
:..2..>.".1. (X )(X ) SINCE A=1":..B.A
>.L.1.4000:..T.F>.".2. (X.-. )(X.-. ) SI
NCE B=.-.5 & C=.+.6":....K>.L.1.4000:...
.P>.".3. (X-3)(X-2) SINCE (-3)+(-2)=-5 &
":..I.Z>." (-3)(-2)=6. ":..Y..>.L.1.400
0:.....>." NOW YOU TRY, FACTORISE X.2.-7
X+12":..+..>.198,0:. " .(RRR)(RRR)";B1$:
."..".X..>.B1$."(X-4)(X-3)".B1$."(X-3)(X
-4)".16160....?." NO, NOT "B1$". .(X-4)(
X-3). IS":.....?." CORRECT. (X-4)(X-3)=X
.2.-3X-4X+12 =":.....?." X.2.-7X+12. LET
'S REVIEW "A1$:.:.15210... ?.9000...*?."
.EXAMPLE 3:. FACTORISE X.2.+X.-.6":..5.
4?.".1. (X )(X ) SINCE A=1":..E.9?.L.1
.4000:..N.>?.".2. (X.+. )(X.-. ) SINCE C
=.-.6":..~.C?.L.1.4000:....H?.".3. (X.+3
.)(X.-2.) SINCE .(+3).+.(-2).=.+1. AND":
..O.R?..18)"(3)(-2)=-6":....W?.L.1.4000:
....\?." SO (X+3)(X-2) ARE THE FACTORS.
NOW YOU":..8.F?." TRY "A1$". FACTORISE X
.2.+X-2":..^.P?.198,0:. " .(RRR)(RRR)";B
1$:.".."...Z?.B1$."(X+2)(X-1)".B1$."(X-1
)(X+2)".16290....?." NO, NOT "B1$", .(X+
2)(X-1).":.....?." IS CORRECT. REMEMBER
"A1$", SIMPLE":.:.15240....?.9040....?."
OK "A1$" WE WILL HAVE A SHORT QUIZ":..K
..?." ON FACTORISATION. THIS TOPIC WILL
BE":..V..?." DEALT WITH FURTHER IN PART
FOUR.":....J?." .MAKE SURE THAT YOU HAVE
PENCIL & PAPER":....T?." "A1$".........
.".J..?.9300.P..?....@.." .THE TOPICS
FOR PART THREE ARE":.:.:..".J..".1 OPER
ATIONS WITH SURDS":..I.T..".2 ALGEBRA I
- SIMPLIFICATION":..P.^.."3 ALGEBRA II
- FACTORISATION":....H..". HAVE YOU ALRE
ADY COMPLETED ANY OF":..F.R.." THESE TOP
ICS "A1$"? ANSWER YES":....|..198,0:. "
OR NO. .RRR";B1$:."."......B1$."NO".."."
:.140......B1$."YES".40080.=...." .TYPE
IN YES OR NO.":.:.40040.M...." DO YOU WI
SH TO START WITH TOPIC 1 FOR":....... "
A REVIEW? .(YES OR NO). .RRR";B2$:."."..
....B2$."YES"..".":.150.I....B2$."NO".40
110......" .TYPE IN YES OR NO.":.:.40080
......" DO YOU WISH TO START WITH TOPIC
2?":..J.... " .(YES OR NO). .R
RR";B3$:.".".E.B..B3$."YES"..".":.40200.
.G..B3$."NO"..".":.40140...H.." .TYPE I
N YES OR NO.":.:.40110.U.L.." THAT LEAVE
S FACTORISATION, BUT TO MAKE":....V.." S
URE THAT YOU'RE READY WE'LL START WITH."
:.440.4...." OK "A1$" JUST TO MAKE SURE
THAT.".J...." YOU KNOW THE MATERIAL WE'L
L START WITH":.:.165.U."..L.1.7...,..532
80,13:.T.1.100:....6..53280,5:.T.1.100:.
:....@..53280,14:..T....T.1.1000:.:.".":
.L.1.7......".........".......9)".PERFEC
T SCORE "A1$......T.1.500:.:.".".'....".
........".D.....9)".PERFECT SCORE "A1$.`
....T.1.500:.:.".":.:.". ".F.&.....
> CLICK IMAGE PREVIEW FOR FULL MODAL