Page 153 - MarceAlgebra Demystified

140 CHAPTER 6 Factoring

2 2
x 7x þ 6 ¼ðx 1Þðx 6Þ. The factors of 6 we need for x þ 5x þ 6 need
2
to sum to 5: x þ 5x þ 6 ¼ðx þ 2Þðx þ 3Þ.
If the second sign is minus, the difference of the factors needs to be the
coefficient of the middle term. If the first sign is plus, the bigger factor will
have the plus sign. If the first sign is minus, the bigger factor will have the
minus sign.

Examples
2
x þ 3x 10: The factors of 10 whose difference is 3 are 2 and 5. The
first sign is plus, so the plus sign goes with 5, the bigger factor:
2
x þ 3x 10 ¼ðx þ 5Þðx 2Þ.

2
x 5x 14: The factors of 14 whose difference is 5 are 2 and 7. The
first sign is minus, so the minus sign goes with 7, the bigger factor:
2
x 5x 14 ¼ðx 7Þðx þ 2Þ.
2
x þ 11x þ 24: 3 8 ¼ 24 and 3 þ 8 ¼ 11
2
x þ 11x þ 24 ¼ðx þ 3Þðx þ 8Þ
2
x 9x þ 18: 3 6 ¼ 18 and 3 þ 6 ¼ 9
2
x 9x þ 18 ¼ðx 3Þðx 6Þ
2
x þ 9x 36: 3 12 ¼ 36 and 12 3 ¼ 9
2
x þ 9x 36 ¼ðx þ 12Þðx 3Þ
2
x 2x 8: 2 4 ¼ 8 and 4 2 ¼ 2

2
x 2x 8 ¼ðx þ 2Þðx 4Þ

Practice

2
1: x 6x þ 9 ¼
2
2: x x 12 ¼
2
3: x þ 9x 22 ¼