1. A Brief Review of Factoring Chapter 5.6

2. 3( ) x 2 2(x)(-6) = -12x GCF = x 2 = 3(x – 6) 2 36 = 2. Are the 1 st and 3 rd terms perfect squares 3. Is 2 nd term double the product of the values whose squares are the 1 st and 3 rd terms √ √ (x) 2 (-6) 2 1a. Factor. 4. Write as a difference squared. 3 – 12 x + 36 Used -6 because the second term is – 12x 3x 2 – 36 x + 108

3. x 4 (x 2 + 1) ( ) 1. GCF = –1 1b. Factor. 9y 2 2. Write as squares 3. (sum)(difference) x 2 – 1 (x 2 + 1)(x + 1) (x – 1) 9x 4 y 2 – 9y 2 9y 2 ( ) 9y 2 9y 2

4. -( ) 4x 2 2(2x)(-3) = -12x GCF = 4x 2 = -(2x – 3) 2 9 = 2. Are the 1 st and 3 rd terms perfect squares 3. Is 2 nd term double the product of the values whose squares are the 1 st and 3 rd terms √ √ (2x) 2 (-3) 2 1c. Factor. 4. Write as a difference squared. -1 – 12 x + 9 Used -3 because the second term is – 12x 12x – 9 – 4x 2 Rewrite it. -4x 2 + 12x – 9

5. 5x 3 (x 2 – 4)( ) 5x 2 5x + 2 1. GCF = -40x 3 -40x 3 5x( ) x 2 – 4 + 2( ) x 2 – 4 (x 2 – 4) (x 2 – 4) – 20x+ 2x 2 – 8 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? YES, now factor. 2. Factor. 1 3. The GCF = 5x 4. The GCF = 2 5. The GCF = (x 2 – 4)

6. 5x 3 (x 2 – 4) 5x + 2 5x( ) x2x2 – 4 + 2( ) x2x2 – 4 – 20x+ 2x 2 – 8 2. Factor. ( ) Difference of Two Squares 2. Write as squares 3. (sum)(difference) (x + 2) (x – 2) (5x + 2)

7. x2x2 1. GCF = (x ) (x ) – 9– 8 2. Factor first term. 3a. Factor. 1 3. Find 2 integers whose product is -8 and sum is -9. 1, -8 2, -4 4, -2 8, -1 x There are none, it can’t be factored. Prime

8. 25x 2 2(5x)(2) = 20x GCF = 25x 2 = Not a perfect square trinomial 4 = 2. Are the 1 st and 3 rd terms perfect squares 3. Is 2 nd term double the product of the values whose squares are the 1 st and 3 rd terms √ (5x) 2 (2) 2 3b. Factor. 20x ≠ 82x 1 + 82 x + 4 Use trial and error or the grouping method

9. 25 3b. Factor. 1. GCF = 2. Grouping Number. 1 (25)(4) 3. Find 2 integers whose product is 100 and sum is 82. 1, 100 2, 50 5, 20 10, 10 x2x2 + 82x + 4 = 100 There are none, it can’t be factored. Prime

10. 64x 2 + 1 Prime Extra. Factor. 1. GCF = Not a difference of two squares, it can’t be factored. 1

11. A Brief Review of Factoring Chapter 5.6