Polynomials Factoring Cheat Sheet Page 3
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4Factoring by grouping:
(1) Group like terms having a common factor and factor it out
(2) Look for a common factor between your factored groups
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Example:
factor 5x + 5y + x
+ xy
Group the y’s together, and the remaining x’s together:
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5y + xy +
5x + x
y(5 + x) +
x(5 + x)
note (5 + x) in common
(y + x)(5 + x)
(always check by multiplying your answer to see if you get the original problem)
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Factoring ax
+ bx + c by “the Box”
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Illustrate by example: factor 8x
– 2x – 15
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Set up the box:
| 8x
|
|
-2x
|
| -15 |
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Multiply down diagonal
-120x
List all the factors of -120x2 and find the ones that add to -2x; the list
shown is the complete one, but you can often see the pattern and shortcut it:
-1x
120x
119x
1x
-120x
-119x
2x
-60x
-58x
-2x
60x
58x
3x
-40x
-37x
-3x
40x
37x
4x
-30x
-26x
-4x
30x
26x
5x
-24x
-19x
-5x
24x
19x
6x
-20x
-14x
-6x
20x
14x
8x
-15x
-7x
-8x
15x
7x
10x
-12x
-2x
<<<< that’s it!!!
-10x
12x
2x
Put the two factors in the other two box spaces (doesn’t matter which):
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| 8x
| 10x |
| -12x | -15 |
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