Page 136 - MarceAlgebra Demystified

CHAPTER 6 Factoring 123

2
4: 4x þ 4x ¼
3 2
5: 4x 6x þ 12x ¼
2 2
6: 24xy þ 6x þ 18x ¼
4 2
7: 30x 6x ¼
3 2 7 2 4 4 2 6
8: 15x y z 30xy z þ 6x y z ¼

Solutions

1: 4x 10y ¼ 2 2x 2 5y ¼ 2ð2x 5yÞ

2: 3x þ 6y 12 ¼ 3 x þ 3 2y 3 4 ¼ 3ðx þ 2y 4Þ
2 2 2
3: 5x þ 15 ¼ 5 x þ 5 3 ¼ 5ðx þ 3Þ
2
4: 4x þ 4x ¼ 4x x þ 4x 1 ¼ 4xðx þ 1Þ

3 2 2 2
5: 4x 6x þ 12x ¼ 2x 2x 2x 3x þ 2x 6 ¼ 2xð2x 3x þ 6Þ
2
2
2
6: 24xy þ 6x þ 18x ¼ 6x ð 4y Þþ 6x x þ 6x 3
2
¼ 6xð 4y þ x þ 3Þ
4 2 2 2 2 2 2
7: 30x 6x ¼ 6x 5x 6x 1 ¼ 6x ð5x 1Þ
2 4
4 2 6
2 4
3 2 7
2 4
2 3
8: 15x y z 30xy z þ 6x y z ¼ 3xy z 5x z 3xy z 10
3 2
2 4
þ 3xy z 2x z
2 4 2 3 3 2
¼ 3xy z ð5x z 10 þ 2x z Þ
Factoring a negative quantity has the same effect on signs within parentheses
as distributing a negative quantity does—every sign changes. Negative quan-
tities are factored in the next examples and practice problems.
Examples

x þ y ¼ ð x yÞ 4 þ x ¼ ð4 xÞ