Page 135 - MarceAlgebra Demystified

122 CHAPTER 6 Factoring

each term as a product of the factor and something else (this step will
become unnecessary once you are experienced). Third apply the distribu-
tion property in reverse.

Examples

4 þ 6x

Each term is divisible by 2, so factor 2 from 4 and 6x:4 þ 6x ¼ 2 2 þ
2 3x ¼ 2ð2 þ 3xÞ:
2
2x þ 5x ¼ x 2 þ x 5x ¼ xð2 þ 5xÞ
2
3x þ 6x ¼ 3x x þ 3x 2 ¼ 3xðx þ 2Þ

8x þ 8 ¼ 8 x þ 8 1 ¼ 8ðx þ 1Þ

2 2 2 2
4xy þ 6x þ 2xy ¼ 2x 2y þ 2x 3x þ 2x y ¼ 2xð2y þ 3x þ y Þ
Complicated expressions can be factored in several steps. Take for
4
5 3 6
6 2
3
example 48x y z þ 60x yz þ 36x y z, each term is divisible by
12xyz. Start with this.
4
5 3 6
3
6 2
3 2
4 2 5
48x y z þ 60x yz þ 36x y z ¼ 12xyz 4x y z þ 12xyz 5x z
5 4 2 5 3 2 5
þ 12xyz 3x y ¼ 12xyzð4x y z þ 5x z þ 3x yÞ
2
Each term in the parentheses is divisible by x :
2
3
2
2
2 2 5
2
3 2
4 2 5
5
4x y z þ 5x z þ 3x y ¼ x 4x y z þ x 5xz þ x 3x y
2 2 2 5 2 3
¼ x ð4x y z þ 5xz þ 3x yÞ
5 3 6 4 3 6 2 2 2 2 5 2 3
48x y z þ 60x yz þ 36x y z ¼ 12xyz x ð4x y z þ 5xz þ 3x yÞ
3 2 2 5 2 3
¼ 12x yzð4x y z þ 5xz þ 3x yÞ
Practice
1: 4x 10y ¼
2: 3x þ 6y 12 ¼
2
3: 5x þ 15 ¼