Page 142 - MarceAlgebra Demystified

CHAPTER 6 Factoring 129

Solutions

2
1: 6xy þ 4xy þ 9xy þ 6x ¼ 2xyð3y þ 2Þþ 3xð3y þ 2Þ
¼ð2xy þ 3xÞð3y þ 2Þ¼ xð2y þ 3Þð3y þ 2Þ

3 2 2 2
2: x þ x x 1 ¼ x ðx þ 1Þ 1ðx þ 1Þ¼ðx 1Þðx þ 1Þ

3: 15xy þ 5x þ 6y þ 2 ¼ 5xð3y þ 1Þþ 2ð3y þ 1Þ
¼ð5x þ 2Þð3y þ 1Þ
4 3 3 3 3
4: 2x 6x x y þ 3y ¼ 2xðx 3Þ yðx 3Þ¼ð2x yÞðx 3Þ
3 2 2 2
5: 9x þ 18x x 2 ¼ 9x ðx þ 2Þ 1ðx þ 2Þ¼ð9x 1Þðx þ 2Þ

Factoring to Reduce Fractions

Among factoring’s many uses is in reducing fractions. If the numerator’s
terms and the denominator’s terms have common factors, factor them then
cancel. It might not be necessary to factor the numerator and denominator
completely.

Examples

2
6x þ 2xy Each term in the numerator and denominator
2
4x y 10xy has a factor of 2x:
2
6x þ 2xy 2xð3x þ yÞ 3x þ y
¼ ¼
2
4x y 10xy 2xð2xy 5yÞ 2xy 5y
xy x xðy 1Þ y 1
¼ ¼
2
16x xy xð16x yÞ 16x y

Practice

18x 24y
1: ¼
6