Page 157 - MarceAlgebra Demystified

144 CHAPTER 6 Factoring

4
4: 256x 1 ¼
4
5: x 81 ¼
4
6: 81x 1 ¼
1 6
7: x 1 ¼
64

4
8: 16x 81 ¼
16
4
9: x 16 ¼
81
12
10: x 1 ¼

Solutions

4 2 2 2
1: x 1 ¼ðx 1Þðx þ 1Þ¼ðx 1Þðx þ 1Þðx þ 1Þ
8 4 4 2 2 4
2: x 16 ¼ðx 4Þðx þ 4Þ¼ðx 2Þðx þ 2Þðx þ 4Þ
1 1 1 1 1 1
8 4 4 2 2 4
3: x ¼ x x þ ¼ x x þ x þ
16 4 4 2 2 4
4 2 2 2
4: 256x 1 ¼ð16x 1Þð16x þ 1Þ¼ð4x 1Þð4x þ 1Þð16x þ 1Þ
4 2 2 2
5: x 81 ¼ðx 9Þðx þ 9Þ¼ðx 3Þðx þ 3Þðx þ 9Þ
4 2 2 2
6: 81x 1 ¼ð9x 1Þð9x þ 1Þ¼ð3x 1Þð3x þ 1Þð9x þ 1Þ
1 1 1
6
3
3
7: x 1 ¼ x 1 x þ 1
64 8 8
4 2 2 2
8: 16x 81 ¼ð4x 9Þð4x þ 9Þ¼ð2x 3Þð2x þ 3Þð4x þ 9Þ
16 4 4
2
2
4
9: x 16 ¼ x 4 x þ 4
81 9 9

2 2 4 2
¼ x 2 x þ 2 x þ 4
3 3 9