Page 156 - MarceAlgebra Demystified

CHAPTER 6 Factoring 143

2
3: x 25 ¼ðx 5Þðx þ 5Þ
2
4: x 64 ¼ðx 8Þðx þ 8Þ
2
5: x 1 ¼ðx 1Þðx þ 1Þ
p p
2 ffiffiffiffiffi ffiffiffiffiffi
6: x 15 ¼ðx 15Þðx þ 15Þ
2
7: 25 x ¼ð5 xÞð5 þ xÞ
n
n
The difference of two squares can come in the form x c where n is any
n
n
even number. The factorization is x c ¼ðx n=2 c n=2 Þðx n=2 þ c n=2 Þ. [When
n
n
n is odd, x c can be factored also but this factorization will not be covered
here.]
Examples

6 6 6 3 3
x 1 ¼ x 1 ¼ðx 1Þðx þ 1Þ
4 4 4 2 2 2 2 2 2
16 x ¼ 2 x ¼ð2 x Þð2 þ x Þ¼ð4 x Þð4 þ x Þ
2
¼ð2 xÞð2 þ xÞð4 þ x Þ
4 4 4 2 2 2
16x 1 ¼ð2xÞ 1 ¼ð4x 1Þð4x þ 1Þ¼ð2x 1Þð2x þ 1Þð4x þ 1Þ
6

1 1 1 1
6 6 3 3
x ¼ x ¼ x x þ
64 2 2 2
10
5
5
10
x 1 ¼ x 1 10 ¼ðx 1Þðx þ 1Þ
8 8 8 4 4 2 2 4
x 1 ¼ x 1 ¼ðx 1Þðx þ 1Þ¼ ðx 1Þðx þ 1Þðx þ 1Þ
2 4
¼ðx 1Þðx þ 1Þðx þ 1Þðx þ 1Þ
Practice

4
1: x 1 ¼

8
2: x 16 ¼
1
8
3: x ¼
16