Interactive Algebra & Trigonometry - A Self Guided Study Companion

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`100%`	file	data	default
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|00000dc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000dd0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 32 20 20 |        |   .22  |
|00000de0| 20 20 20 20 20 20 20 20 | 20 20 20 32 0d 0b 00 11 |        |   2....|
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|00000e10| 78 20 20 11 31 2b 20 11 | 33 62 78 20 11 31 2b 20 |x  .1+ .|3bx .1+ |
|00000e20| 11 33 63 20 11 31 3d 20 | 11 33 78 20 20 11 31 2d |.3c .1= |.3x  .1-|
|00000e30| 20 31 31 11 33 78 20 11 | 31 2b 20 32 34 2e 20 20 | 11.3x .|1+ 24.  |
|00000e40| 54 68 75 73 2c 20 11 33 | 61 20 11 31 3d 20 31 2c |Thus, .3|a .1= 1,|
|00000e50| 20 0d 0a 00 11 33 62 20 | 11 31 3d 20 2d 31 31 2c | ....3b |.1= -11,|
|00000e60| 20 61 6e 64 20 11 33 63 | 20 11 31 3d 20 32 34 2e | and .3c| .1= 24.|
|00000e70| 13 0d 0a 00 0d 0b 00 53 | 69 6e 63 65 20 11 33 62 |.......S|ince .3b|
|00000e80| 20 11 31 69 73 20 6e 65 | 67 61 74 69 76 65 20 61 | .1is ne|gative a|
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|00000eb0| 72 73 20 6f 66 20 32 34 | 20 6d 75 73 74 20 62 65 |rs of 24| must be|
|00000ec0| 20 6e 65 67 61 74 69 76 | 65 2e 0d 0a 00 54 68 61 | negativ|e....Tha|
|00000ed0| 74 20 69 73 2c 20 32 34 | 20 3d 20 28 2d 31 29 28 |t is, 24| = (-1)(|
|00000ee0| 2d 32 34 29 2c 20 32 34 | 20 3d 20 28 2d 32 29 28 |-24), 24| = (-2)(|
|00000ef0| 2d 31 32 29 2c 20 32 34 | 20 3d 20 28 2d 33 29 28 |-12), 24| = (-3)(|
|00000f00| 2d 38 29 2c 20 6f 72 20 | 32 34 20 3d 20 28 2d 34 |-8), or |24 = (-4|
|00000f10| 29 28 2d 36 29 2e 13 0d | 0a 00 0d 0b 00 54 68 65 |)(-6)...|.....The|
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|00000f40| 6f 6e 73 20 61 72 65 0d | 0a 00 0d 0b 00 20 20 28 |ons are.|.....  (|
|00000f50| 11 33 78 20 11 31 2d 20 | 31 29 28 11 33 78 20 11 |.3x .1- |1)(.3x .|
|00000f60| 31 2d 20 32 34 29 2c 20 | 20 28 11 33 78 20 11 31 |1- 24), | (.3x .1|
|00000f70| 2d 20 32 29 28 11 33 78 | 20 11 31 2d 20 31 32 29 |- 2)(.3x| .1- 12)|
|00000f80| 2c 20 20 28 11 33 78 20 | 11 31 2d 20 33 29 28 11 |,  (.3x |.1- 3)(.|
|00000f90| 33 78 20 11 31 2d 20 38 | 29 2c 20 20 61 6e 64 20 |3x .1- 8|),  and |
|00000fa0| 20 28 11 33 78 20 11 31 | 2d 20 34 29 28 11 33 78 | (.3x .1|- 4)(.3x|
|00000fb0| 20 11 31 2d 20 36 29 2e | 13 0d 0a 00 0d 0b 00 54 | .1- 6).|.......T|
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|00000fd0| 65 20 74 65 72 6d 2c 20 | 77 65 20 66 69 6e 64 20 |e term, |we find |
|00000fe0| 74 68 65 20 63 6f 72 72 | 65 63 74 20 66 61 63 74 |the corr|ect fact|
|00000ff0| 6f 72 69 7a 61 74 69 6f | 6e 20 74 6f 20 62 65 0d |orizatio|n to be.|
|00001000| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00001010| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 |      .2|2...    |
|00001020| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001030| 33 78 20 20 11 31 2d 20 | 31 31 11 33 78 20 11 31 |3x  .1- |11.3x .1|
|00001040| 2b 20 32 34 20 3d 20 28 | 11 33 78 20 11 31 2d 20 |+ 24 = (|.3x .1- |
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|00001080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001090| 20 11 32 32 0d 0b 00 11 | 31 46 61 63 74 6f 72 20 | .22....|1Factor |
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|000010f0| 20 20 20 20 20 20 20 11 | 32 32 20 20 20 20 20 20 |       .|22      |
|00001100| 20 20 20 20 20 20 20 20 | 32 0d 0b 00 11 31 46 6f |        |2....1Fo|
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|00001120| 2c 20 77 65 20 68 61 76 | 65 20 11 33 61 78 20 20 |, we hav|e .3ax  |
|00001130| 11 31 2b 20 11 33 62 78 | 20 11 31 2b 20 11 33 63 |.1+ .3bx| .1+ .3c|
|00001140| 20 11 31 3d 20 32 11 33 | 78 20 20 11 31 2b 20 35 | .1= 2.3|x  .1+ 5|
|00001150| 11 33 78 20 11 31 2d 20 | 33 2e 20 20 54 68 75 73 |.3x .1- |3.  Thus|
|00001160| 2c 20 11 33 61 20 11 31 | 3d 20 32 2c 20 11 33 62 |, .3a .1|= 2, .3b|
|00001170| 20 11 31 3d 20 35 2c 0d | 0a 00 61 6e 64 20 11 33 | .1= 5,.|..and .3|
|00001180| 63 20 11 31 3d 20 2d 33 | 2e 13 0d 0a 00 0d 0b 00 |c .1= -3|........|
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|00001240| 31 2b 20 31 29 28 11 33 | 78 20 11 31 2d 20 33 29 |1+ 1)(.3|x .1- 3)|
|00001250| 20 20 20 20 20 28 32 11 | 33 78 20 11 31 2b 20 33 |     (2.|3x .1+ 3|
|00001260| 29 28 11 33 78 20 11 31 | 2d 20 31 29 20 20 20 20 |)(.3x .1|- 1)    |
|00001270| 20 28 32 11 33 78 20 11 | 31 2d 20 31 29 28 11 33 | (2.3x .|1- 1)(.3|
|00001280| 78 20 11 31 2b 20 33 29 | 20 20 20 20 20 28 32 11 |x .1+ 3)|     (2.|
|00001290| 33 78 20 11 31 2d 20 33 | 29 28 11 33 78 20 11 31 |3x .1- 3|)(.3x .1|
|000012a0| 2b 20 31 29 13 0d 0a 00 | 0d 0b 00 54 65 73 74 69 |+ 1)....|...Testi|
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|000012d0| 63 6f 72 72 65 63 74 20 | 66 61 63 74 6f 72 69 7a |correct |factoriz|
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|00001300| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 |      .2|2...    |
|00001310| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001320| 20 20 11 31 32 11 33 78 | 20 20 11 31 2b 20 35 11 |  .12.3x|  .1+ 5.|
|00001330| 33 78 20 11 31 2d 20 33 | 20 3d 20 28 32 11 33 78 |3x .1- 3| = (2.3x|
|00001340| 20 11 31 2d 20 31 29 28 | 11 33 78 20 11 31 2b 20 | .1- 1)(|.3x .1+ |
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|00001360| 34 20 20 46 61 63 74 6f | 72 69 6e 67 0d 0b 00 20 |4  Facto|ring... |
|00001370| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001380| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001390| 32 32 20 20 20 20 33 0d | 0b 00 11 31 46 61 63 74 |22    3.|...1Fact|
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|000013b0| 6c 20 33 20 2b 20 11 33 | 78 20 11 31 2d 20 33 11 |l 3 + .3|x .1- 3.|
|000013c0| 33 78 20 20 11 31 2d 20 | 11 33 78 20 20 11 31 62 |3x  .1- |.3x  .1b|
|000013d0| 79 20 67 72 6f 75 70 69 | 6e 67 2e 0d 0a 00 0d 0a |y groupi|ng......|
|000013e0| 00 13 12 31 53 4f 4c 55 | 54 49 4f 4e 12 30 0d 0a |...1SOLU|TION.0..|
|000013f0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00001400| 20 20 20 11 32 32 20 20 | 20 20 33 20 20 20 20 20 |   .22  |  3     |
|00001410| 20 20 20 20 20 20 20 20 | 20 20 20 32 20 20 20 20 |        |   2    |
|00001420| 33 0d 0b 00 20 20 20 20 | 20 20 20 20 11 31 33 20 |3...    |    .13 |
|00001430| 2b 20 11 33 78 20 11 31 | 2d 20 33 11 33 78 20 20 |+ .3x .1|- 3.3x  |
|00001440| 11 31 2d 20 11 33 78 20 | 20 11 31 3d 20 28 33 20 |.1- .3x | .1= (3 |
|00001450| 2b 20 11 33 78 11 31 29 | 20 2d 20 28 33 11 33 78 |+ .3x.1)| - (3.3x|
|00001460| 20 20 11 31 2b 20 11 33 | 78 20 11 31 29 20 20 20 |  .1+ .3|x .1)   |
|00001470| 20 20 20 20 20 20 12 31 | 11 32 47 72 6f 75 70 20 |      .1|.2Group |
|00001480| 74 65 72 6d 73 11 31 12 | 30 13 0d 0a 00 0d 0a 00 |terms.1.|0.......|
|00001490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000014a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000014b0| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 |      .2|2...    |
|000014c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000014d0| 20 20 20 20 20 11 31 3d | 20 28 33 20 2b 20 11 33 |     .1=| (3 + .3|
|000014e0| 78 11 31 29 20 2d 20 11 | 33 78 20 11 31 28 33 20 |x.1) - .|3x .1(3 |
|000014f0| 2b 20 11 33 78 20 11 31 | 29 20 20 20 20 20 20 20 |+ .3x .1|)       |
|00001500| 20 20 12 31 11 32 46 61 | 63 74 6f 72 20 67 72 6f |  .1.2Fa|ctor gro|
|00001510| 75 70 73 11 31 12 30 13 | 0d 0a 00 0d 0a 00 20 20 |ups.1.0.|......  |
|00001520| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001530| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001540| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 |      .2|2...    |
|00001550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001560| 20 20 20 20 20 11 31 3d | 20 28 33 20 2b 20 11 33 |     .1=| (3 + .3|
|00001570| 78 11 31 29 28 31 20 2d | 20 11 33 78 20 11 31 29 |x.1)(1 -| .3x .1)|
|00001580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 12 31 |        |      .1|
|00001590| 11 32 52 65 6d 6f 76 65 | 20 63 6f 6d 6d 6f 6e 20 |.2Remove| common |
|000015a0| 62 69 6e 6f 6d 69 61 6c | 11 31 12 30 0d 0a 00 20 |binomial|.1.0... |
|000015b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015e0| 20 20 20 20 20 20 20 12 | 31 11 32 66 61 63 74 6f |       .|1.2facto|
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|00001600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001610| 20 20 20 20 20 20 20 20 | 3d 20 28 33 20 2b 20 11 |        |= (3 + .|
|00001620| 33 78 11 31 29 28 31 20 | 2b 20 11 33 78 11 31 29 |3x.1)(1 |+ .3x.1)|
|00001630| 28 31 20 2d 20 11 33 78 | 11 31 29 20 20 20 20 20 |(1 - .3x|.1)     |
|00001640| 20 20 20 12 31 11 32 46 | 61 63 74 6f 72 20 64 69 |   .1.2F|actor di|
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|00001660| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00001670| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001690| 20 20 20 20 20 20 20 20 | 20 20 20 12 31 11 32 74 |        |   .1.2t|
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|000016f0| 2d 20 38 11 33 79 20 20 | 11 31 2b 20 33 11 33 79 |- 8.3y  |.1+ 3.3y|
|00001700| 20 11 31 2d 20 31 32 2e | 0d 0a 00 0d 0a 00 13 12 | .1- 12.|........|
|00001710| 31 53 4f 4c 55 54 49 4f | 4e 12 30 0d 0a 00 20 20 |1SOLUTIO|N.0...  |
|00001720| 11 32 34 20 20 20 20 20 | 33 20 20 20 20 20 20 20 |.24     |3       |
|00001730| 20 20 20 20 20 20 20 20 | 20 34 20 20 20 20 20 33 |        | 4     3|
|00001740| 0d 0b 00 11 31 32 11 33 | 79 20 20 11 31 2d 20 38 |....12.3|y  .1- 8|
|00001750| 11 33 79 20 20 11 31 2b | 20 33 11 33 79 20 11 31 |.3y  .1+| 3.3y .1|
|00001760| 2d 20 31 32 20 3d 20 28 | 32 11 33 79 20 20 11 31 |- 12 = (|2.3y  .1|
|00001770| 2d 20 38 11 33 79 20 11 | 31 29 20 2b 20 28 33 11 |- 8.3y .|1) + (3.|
|00001780| 33 79 20 11 31 2d 20 31 | 32 29 20 20 20 20 20 20 |3y .1- 1|2)      |
|00001790| 20 20 20 20 20 12 31 11 | 32 47 72 6f 75 70 20 74 |     .1.|2Group t|
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|000017c0| 20 20 20 20 20 20 20 11 | 32 33 0d 0b 00 20 20 20 |       .|23...   |
|000017d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000017e0| 20 11 31 3d 20 32 11 33 | 79 20 11 31 28 11 33 79 | .1= 2.3|y .1(.3y|
|000017f0| 20 11 31 2d 20 34 29 20 | 2b 20 33 28 11 33 79 20 | .1- 4) |+ 3(.3y |
|00001800| 11 31 2d 20 34 29 20 20 | 20 20 20 20 20 20 20 20 |.1- 4)  |        |
|00001810| 20 20 20 12 31 11 32 46 | 61 63 74 6f 72 20 67 72 |   .1.2F|actor gr|
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|00001830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001840| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001850| 32 33 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |23...   |        |
|00001860| 20 20 20 20 20 20 20 20 | 20 11 31 3d 20 28 11 33 |        | .1= (.3|
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|00001880| 31 2b 20 33 29 20 20 20 | 20 20 20 20 20 20 20 20 |1+ 3)   |        |
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|00001970| 35 2c 20 77 68 69 63 68 | 20 69 6d 70 6c 69 65 73 |5, which| implies|
|00001980| 20 74 68 61 74 20 74 68 | 65 20 70 72 6f 64 75 63 | that th|e produc|
|00001990| 74 0d 0a 00 11 33 61 63 | 20 11 31 3d 20 2d 39 30 |t....3ac| .1= -90|
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|00001a10| 30 20 3d 20 2d 31 20 3d | 20 11 33 62 11 31 2c 20 |0 = -1 =| .3b.1, |
|00001a20| 77 65 20 72 65 77 72 69 | 74 65 20 74 68 65 20 6d |we rewri|te the m|
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|00001a40| 74 68 65 20 74 72 69 6e | 6f 6d 69 61 6c 20 61 73 |the trin|omial as|
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|00001a60| 20 20 2d 11 33 78 20 11 | 31 3d 20 39 11 33 78 20 |  -.3x .|1= 9.3x |
|00001a70| 11 31 2d 20 31 30 11 33 | 78 11 31 2e 13 0d 0a 00 |.1- 10.3|x.1.....|
|00001a80| 0d 0b 00 54 68 69 73 20 | 70 72 6f 64 75 63 65 73 |...This |produces|
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|00001aa0| 0a 00 20 20 20 20 20 20 | 20 11 32 32 20 20 20 20 |..      | .22    |
|00001ab0| 20 20 20 20 20 20 20 20 | 20 20 32 0d 0b 00 20 20 |        |  2...  |
|00001ac0| 20 20 20 11 31 36 11 33 | 78 20 20 11 31 2d 20 11 |   .16.3|x  .1- .|
|00001ad0| 33 78 20 11 31 2d 20 31 | 35 20 3d 20 36 11 33 78 |3x .1- 1|5 = 6.3x|
|00001ae0| 20 20 11 31 2b 20 39 11 | 33 78 20 11 31 2d 20 31 |  .1+ 9.|3x .1- 1|
|00001af0| 30 11 33 78 20 11 31 2d | 20 31 35 20 20 20 20 20 |0.3x .1-| 15     |
|00001b00| 20 20 20 20 12 31 11 32 | 52 65 77 72 69 74 65 20 |    .1.2|Rewrite |
|00001b10| 6d 69 64 64 6c 65 20 74 | 65 72 6d 11 31 12 30 13 |middle t|erm.1.0.|
|00001b20| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00001b30| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|00001b40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001b50| 20 20 11 31 3d 20 28 36 | 11 33 78 20 20 11 31 2b |  .1= (6|.3x  .1+|
|00001b60| 20 39 11 33 78 11 31 29 | 20 2d 20 28 31 30 11 33 | 9.3x.1)| - (10.3|
|00001b70| 78 20 11 31 2b 20 31 35 | 29 20 20 20 20 20 12 31 |x .1+ 15|)     .1|
|00001b80| 11 32 47 72 6f 75 70 20 | 74 65 72 6d 73 11 31 12 |.2Group |terms.1.|
|00001b90| 30 13 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 20 |0.......|        |
|00001ba0| 20 20 20 20 20 20 20 20 | 20 20 3d 20 33 11 33 78 |        |  = 3.3x|
|00001bb0| 11 31 28 32 11 33 78 20 | 11 31 2b 20 33 29 20 2d |.1(2.3x |.1+ 3) -|
|00001bc0| 20 35 28 32 11 33 78 20 | 11 31 2b 20 33 29 20 20 | 5(2.3x |.1+ 3)  |
|00001bd0| 20 20 20 20 12 31 11 32 | 46 61 63 74 6f 72 20 67 |    .1.2|Factor g|
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|00001bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001c00| 20 20 3d 20 28 32 11 33 | 78 20 11 31 2b 20 33 29 |  = (2.3|x .1+ 3)|
|00001c10| 28 33 11 33 78 20 11 31 | 2d 20 35 29 20 20 20 20 |(3.3x .1|- 5)    |
|00001c20| 20 20 20 20 20 20 20 20 | 12 31 11 32 52 65 6d 6f |        |.1.2Remo|
|00001c30| 76 65 20 63 6f 6d 6d 6f | 6e 20 62 69 6e 6f 6d 69 |ve commo|n binomi|
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|00001c60| 74 6f 72 69 6e 67 0d 0b | 00 46 61 63 74 6f 72 20 |toring..|.Factor |
|00001c70| 74 68 65 20 66 6f 6c 6c | 6f 77 69 6e 67 20 70 6f |the foll|owing po|
|00001c80| 6c 79 6e 6f 6d 69 61 6c | 73 2e 0d 0a 00 0d 0b 00 |lynomial|s.......|
|00001c90| 20 20 20 20 20 20 11 32 | 33 20 20 20 11 31 31 20 |      .2|3   .11 |
|00001ca0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001cb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001cc0| 20 20 11 32 33 0d 0b 00 | 11 31 28 61 29 20 20 11 |  .23...|.1(a)  .|
|00001cd0| 33 78 20 20 11 31 2d 20 | 11 34 32 20 20 20 20 20 |3x  .1- |.42     |
|00001ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001cf0| 11 31 28 62 29 20 20 32 | 37 20 2b 20 31 32 35 11 |.1(b)  2|7 + 125.|
|00001d00| 33 79 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 11 |3y...   |       .|
|00001d10| 31 38 0d 0a 00 0d 0b 00 | 13 12 31 53 4f 4c 55 54 |18......|..1SOLUT|
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|00001d30| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001d40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001d50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001d60| 20 20 20 11 32 33 0d 0b | 00 11 31 61 29 20 54 68 |   .23..|..1a) Th|
|00001d70| 69 73 20 70 6f 6c 79 6e | 6f 6d 69 61 6c 20 69 73 |is polyn|omial is|
|00001d80| 20 74 68 65 20 64 69 66 | 66 65 72 65 6e 63 65 20 | the dif|ference |
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|00001e30| 33 20 20 20 11 31 31 20 | 20 20 20 11 32 33 20 20 |3   .11 |   .23  |
|00001e40| 20 11 34 28 11 31 31 11 | 34 29 11 32 33 0d 0b 00 | .4(.11.|4).23...|
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|00001e60| 20 11 34 32 20 11 31 3d | 20 11 33 78 20 20 11 31 | .42 .1=| .3x  .1|
|00001e70| 2d 20 11 34 21 32 21 20 | 20 20 20 20 20 20 20 20 |- .4!2! |        |
|00001e80| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 12 31 11 |        |   .1.1.|
|00001e90| 32 57 72 69 74 65 20 61 | 73 20 64 69 66 66 65 72 |2Write a|s differ|
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|00001ec0| 20 20 20 20 20 38 20 20 | 20 20 20 20 20 20 11 34 |     8  |      .4|
|00001ed0| 39 11 31 32 11 34 30 20 | 20 20 20 20 20 20 20 20 |9.12.40 |        |
|00001ee0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001ef0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001f00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001f10| 20 11 31 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | .1.... |        |
|00001f20| 20 20 20 20 20 20 20 20 | 11 34 28 20 20 20 20 11 |        |.4(    .|
|00001f30| 31 31 11 34 29 28 20 11 | 32 32 20 20 20 11 31 31 |11.4)( .|22   .11|
|00001f40| 20 20 20 20 11 34 28 11 | 31 31 11 34 29 11 32 32 |    .4(.|11.4).22|
|00001f50| 11 34 29 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |.4)...  |        |
|00001f60| 20 20 20 20 20 11 31 3d | 20 11 34 21 11 33 78 20 |     .1=| .4!.3x |
|00001f70| 11 31 2d 20 11 34 32 21 | 21 11 33 78 20 20 11 31 |.1- .42!|!.3x  .1|
|00001f80| 2b 20 11 34 32 11 33 78 | 20 11 31 2b 20 11 34 21 |+ .42.3x| .1+ .4!|
|00001f90| 32 21 20 21 20 20 20 20 | 20 11 31 12 31 11 32 46 |2! !    | .1.1.2F|
|00001fa0| 61 63 74 6f 72 65 64 20 | 66 6f 72 6d 11 31 12 30 |actored |form.1.0|
|00001fb0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00001fc0| 20 20 20 20 11 34 39 20 | 20 20 20 11 31 32 11 34 |    .49 |   .12.4|
|00001fd0| 30 39 20 20 20 20 20 11 | 31 32 20 20 20 20 11 34 |09     .|12    .4|
|00001fe0| 39 11 31 32 11 34 30 20 | 30 20 20 20 20 20 20 20 |9.12.40 |0       |
|00001ff0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002000| 20 11 31 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | .1.... |        |
|00002010| 20 20 20 20 20 20 20 20 | 11 34 28 20 20 20 20 11 |        |.4(    .|
|00002020| 31 31 11 34 29 28 20 11 | 32 32 20 20 20 11 31 31 |11.4)( .|22   .11|
|00002030| 20 20 20 20 31 11 34 29 | 0d 0b 00 20 20 20 20 20 |    1.4)|...     |
|00002040| 20 20 20 20 20 20 20 20 | 20 20 11 31 3d 20 11 34 |        |  .1= .4|
|00002050| 21 11 33 78 20 11 31 2d | 20 11 34 32 21 21 11 33 |!.3x .1-| .42!!.3|
|00002060| 78 20 20 11 31 2b 20 11 | 34 32 11 33 78 20 11 31 |x  .1+ .|42.3x .1|
|00002070| 2b 20 11 34 32 21 20 20 | 20 20 20 20 20 20 11 31 |+ .42!  |      .1|
|00002080| 12 31 11 32 53 69 6d 70 | 6c 69 66 79 11 31 12 30 |.1.2Simp|lify.1.0|
|00002090| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|000020a0| 20 20 20 20 11 34 39 20 | 20 20 20 11 31 32 11 34 |    .49 |   .12.4|
|000020b0| 30 39 20 20 20 20 20 11 | 31 32 20 20 20 20 34 11 |09     .|12    4.|
|000020c0| 34 30 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |40      |        |
|000020d0| 20 20 20 20 20 20 20 20 | 11 31 13 0d 0a 00 0d 0b |        |.1......|
|000020e0| 00 62 29 20 54 68 69 73 | 20 70 6f 6c 79 6e 6f 6d |.b) This| polynom|
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|00002130| 20 20 20 20 20 20 11 32 | 33 0d 0b 00 20 20 20 11 |      .2|3...   .|
|00002140| 31 31 32 35 11 33 79 20 | 20 11 31 69 73 20 74 68 |1125.3y | .1is th|
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|00002160| 2e 0d 0a 00 0d 0b 00 20 | 20 20 54 68 65 72 65 66 |....... |  Theref|
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|00002180| 6f 72 20 74 68 65 20 70 | 6f 6c 79 6e 6f 6d 69 61 |or the p|olynomia|
|00002190| 6c 20 61 73 20 66 6f 6c | 6c 6f 77 73 2e 0d 0a 00 |l as fol|lows....|
|000021a0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|000021b0| 20 11 32 33 20 20 20 20 | 33 20 20 20 20 20 20 20 | .23    |3       |
|000021c0| 33 0d 0b 00 20 20 20 20 | 20 11 31 32 37 20 2b 20 |3...    | .127 + |
|000021d0| 31 32 35 11 33 79 20 20 | 11 31 3d 20 33 20 20 2b |125.3y  |.1= 3  +|
|000021e0| 20 28 35 11 33 79 11 31 | 29 20 20 20 20 20 20 20 | (5.3y.1|)       |
|000021f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 12 |        |       .|
|00002200| 31 11 32 57 72 69 74 65 | 20 61 73 20 74 68 65 20 |1.2Write| as the |
|00002210| 73 75 6d 20 6f 66 20 74 | 77 6f 20 63 75 62 65 73 |sum of t|wo cubes|
|00002220| 11 31 12 30 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |.1.0... |        |
|00002230| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002240| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00002260| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002270| 20 20 20 20 20 20 20 13 | 0d 0a 00 20 20 20 20 20 |       .|...     |
|00002280| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002290| 20 20 20 20 20 11 34 28 | 20 11 32 32 20 20 20 20 |     .4(| .22    |
|000022a0| 20 20 20 20 20 20 20 20 | 20 20 20 32 11 34 29 0d |        |   2.4).|
|000022b0| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|000022c0| 20 20 11 31 3d 20 28 33 | 20 2b 20 35 11 33 79 11 |  .1= (3| + 5.3y.|
|000022d0| 31 29 11 34 21 11 31 33 | 20 20 2d 20 33 28 35 11 |1).4!.13|  - 3(5.|
|000022e0| 33 79 11 31 29 20 2b 20 | 28 35 11 33 79 11 31 29 |3y.1) + |(5.3y.1)|
|000022f0| 20 11 34 21 20 20 20 11 | 31 12 31 11 32 46 61 63 | .4!   .|1.1.2Fac|
|00002300| 74 6f 72 65 64 20 66 6f | 72 6d 11 31 12 30 0d 0b |tored fo|rm.1.0..|
|00002310| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00002320| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 39 20 20 |        |   .49  |
|00002330| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002340| 30 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |0       |        |
|00002350| 20 20 20 20 20 20 20 11 | 31 13 0d 0a 00 20 20 20 |       .|1....   |
|00002360| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002370| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002380| 20 20 20 20 20 11 32 32 | 0d 0b 00 20 20 20 20 20 |     .22|...     |
|00002390| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 3d 20 28 |        |   .1= (|
|000023a0| 33 20 2b 20 35 11 33 79 | 11 31 29 28 39 20 2d 20 |3 + 5.3y|.1)(9 - |
|000023b0| 31 35 11 33 79 20 11 31 | 2b 20 32 35 11 33 79 20 |15.3y .1|+ 25.3y |
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|00002400| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |        |      .2|
|00002410| 33 20 20 20 20 20 20 32 | 0d 0b 00 11 31 46 61 63 |3      2|....1Fac|
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|00002450| 63 6f 6d 70 6c 65 74 65 | 6c 79 2e 0d 0a 00 0d 0b |complete|ly......|
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|00002470| 00 0d 0b 00 42 65 63 61 | 75 73 65 20 74 68 69 73 |....Beca|use this|
|00002480| 20 74 72 69 6e 6f 6d 69 | 61 6c 20 68 61 73 20 61 | trinomi|al has a|
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|000024c0| 63 74 6f 72 69 6e 67 20 | 6f 75 74 20 74 68 65 20 |ctoring |out the |
|000024d0| 28 6e 65 67 61 74 69 76 | 65 29 20 63 6f 6d 6d 6f |(negativ|e) commo|
|000024e0| 6e 20 6d 6f 6e 6f 6d 69 | 61 6c 20 66 61 63 74 6f |n monomi|al facto|
|000024f0| 72 20 2d 33 11 33 78 11 | 31 2e 0d 0a 00 20 20 20 |r -3.3x.|1....   |
|00002500| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 33 20 20 |        |   .23  |
|00002510| 20 20 20 20 32 20 20 20 | 20 20 20 20 20 20 20 20 |    2   |        |
|00002520| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 20 20 20 |    2...|        |
|00002530| 20 20 20 11 31 2d 36 11 | 33 78 20 20 11 31 2b 20 |   .1-6.|3x  .1+ |
|00002540| 31 35 11 33 78 20 20 11 | 31 2b 20 33 36 11 33 78 |15.3x  .|1+ 36.3x|
|00002550| 20 11 31 3d 20 2d 33 11 | 33 78 11 31 28 32 11 33 | .1= -3.|3x.1(2.3|
|00002560| 78 20 20 11 31 2d 20 35 | 11 33 78 20 11 31 2d 20 |x  .1- 5|.3x .1- |
|00002570| 31 32 29 13 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |12).....|..      |
|00002580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002590| 20 20 20 20 20 20 20 11 | 32 32 0d 0b 00 11 31 4e |       .|22....1N|
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|000025b0| 74 72 69 6e 6f 6d 69 61 | 6c 20 32 11 33 78 20 20 |trinomia|l 2.3x  |
|000025c0| 11 31 2d 20 35 11 33 78 | 20 11 31 2d 20 31 32 2c |.1- 5.3x| .1- 12,|
|000025d0| 20 77 65 20 68 61 76 65 | 20 11 33 61 20 11 31 3d | we have| .3a .1=|
|000025e0| 20 32 20 61 6e 64 20 11 | 33 63 20 11 31 3d 20 2d | 2 and .|3c .1= -|
|000025f0| 31 32 2e 13 0d 0a 00 54 | 68 65 20 70 6f 73 73 69 |12.....T|he possi|
|00002600| 62 6c 65 20 66 61 63 74 | 6f 72 69 7a 61 74 69 6f |ble fact|orizatio|
|00002610| 6e 73 20 6f 66 20 74 68 | 69 73 20 74 72 69 6e 6f |ns of th|is trino|
|00002620| 6d 69 61 6c 20 61 72 65 | 20 61 73 20 66 6f 6c 6c |mial are| as foll|
|00002630| 6f 77 73 2e 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |ows.... |        |
|00002640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002650| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 20 20 |        |.22...  |
|00002660| 20 20 20 20 20 20 20 20 | 20 20 11 31 28 32 11 33 |        |  .1(2.3|
|00002670| 78 20 11 31 2b 20 31 29 | 28 11 33 78 20 11 31 2d |x .1+ 1)|(.3x .1-|
|00002680| 20 31 32 29 20 3d 20 32 | 11 33 78 20 20 11 31 2d | 12) = 2|.3x  .1-|
|00002690| 20 32 33 11 33 78 20 11 | 31 2d 20 31 32 13 0d 0a | 23.3x .|1- 12...|
|000026a0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
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|000026d0| 20 20 20 20 20 11 31 28 | 32 11 33 78 20 11 31 2b |     .1(|2.3x .1+|
|000026e0| 20 33 29 28 11 33 78 20 | 11 31 2d 20 34 29 20 3d | 3)(.3x |.1- 4) =|
|000026f0| 20 32 11 33 78 20 20 11 | 31 2d 20 35 11 33 78 20 | 2.3x  .|1- 5.3x |
|00002700| 11 31 2d 20 31 32 20 20 | 20 20 20 20 20 12 31 11 |.1- 12  |     .1.|
|00002710| 32 43 6f 72 72 65 63 74 | 20 66 61 63 74 6f 72 69 |2Correct| factori|
|00002720| 7a 61 74 69 6f 6e 11 31 | 12 30 13 0d 0a 00 0d 0a |zation.1|.0......|
|00002730| 00 54 68 65 72 65 66 6f | 72 65 2c 20 74 68 65 20 |.Therefo|re, the |
|00002740| 63 6f 6d 70 6c 65 74 65 | 6c 79 20 66 61 63 74 6f |complete|ly facto|
|00002750| 72 65 64 20 66 6f 72 6d | 20 6f 66 20 74 68 65 20 |red form| of the |
|00002760| 6f 72 69 67 69 6e 61 6c | 20 74 72 69 6e 6f 6d 69 |original| trinomi|
|00002770| 61 6c 20 69 73 0d 0a 00 | 20 20 20 20 20 20 20 20 |al is...|        |
|00002780| 20 20 20 20 20 20 11 32 | 33 20 20 20 20 20 20 32 |      .2|3      2|
|00002790| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 32 |        |       2|
|000027a0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 11 31 |...     |      .1|
|000027b0| 2d 36 11 33 78 20 20 11 | 31 2b 20 31 35 11 33 78 |-6.3x  .|1+ 15.3x|
|000027c0| 20 20 11 31 2b 20 33 36 | 11 33 78 20 11 31 3d 20 |  .1+ 36|.3x .1= |
|000027d0| 2d 33 11 33 78 11 31 28 | 32 11 33 78 20 20 11 31 |-3.3x.1(|2.3x  .1|
|000027e0| 2d 20 35 11 33 78 20 11 | 31 2d 20 31 32 29 20 3d |- 5.3x .|1- 12) =|
|000027f0| 20 2d 33 11 33 78 11 31 | 28 32 11 33 78 20 11 31 | -3.3x.1|(2.3x .1|
|00002800| 2b 20 33 29 28 11 33 78 | 20 11 31 2d 20 34 29 2e |+ 3)(.3x| .1- 4).|
|00002810| 0d 0a 00 26 00 00 00 a8 | 02 00 00 4d 16 00 00 10 |...&....|...M....|
|00002820| 00 00 00 00 00 00 00 65 | 30 2d 34 00 e4 02 00 00 |.......e|0-4.....|
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|00002850| 16 00 00 9f 06 00 00 00 | 00 00 00 65 30 2d 34 2d |........|...e0-4-|
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|00002870| 00 00 00 00 00 00 65 30 | 2d 34 2d 33 00 5b 0d 00 |......e0|-4-3.[..|
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|00002900| 34 2d 38 00 66 1c 00 00 | 77 07 00 00 4d 16 00 00 |4-8.f...|w...M...|
|00002910| 50 1c 00 00 00 00 00 00 | 69 30 2d 34 2d 31 00 f3 |P.......|i0-4-1..|
|00002920| 23 00 00 20 04 00 00 4d | 16 00 00 dd 23 00 00 00 |#.. ...M|....#...|
|00002930| 00 00 00 69 30 2d 34 2d | 32 00                   |...i0-4-|2.      |
+--------+-------------------------+-------------------------+--------+--------+