Chapter 5 Pretest

Factor each of the following completely xy 2 ( ) 5 5 x 6 – GCF = 5 x7x7 y2y2 – 15 x y2y2 x y 2 xy 2 xy 2

3. Find 2 integers whose product is 10 and sum is 7 1, 10 2, 5 (x )(x ) GCF = 2.x 2 + 7x + 10 Factor each of the following completely Factor first term.

3( ) 2 3 ( 2x 2 + x + 4x + 2 ) 1. GCF = 2. Grouping Number Split into 2 terms. (2)(2) = 3. Find 2 integers whose product is 4 and sum is 5. 1, 4 x 2 + 5x x2x2 + 15x

Factor each of the following completely. (2x + 1)( ) ( ) + 2 ( ) 3 ( ) 3 5. Factor by grouping. 3 x 2 x + 2 x 2x + 1 2x + 1 (2x + 1) (2x + 1) 2x 2 + x + 4x + 2 GCF = GCF = GCF = () x 2 (2x + 1) 3( ) 2 x2x2 + 5x x2x2 + 15x

2(6a)(5b) = 60ab 36a 2 = (6a + 5b) 2 25b 2 = 2. Are the 1 st and 3 rd terms are perfect squares √ 3. Is 2 nd term double the product of the values whose squares are the 1 st and 3 rd terms √ 4.36a ab + 25b 2 Factor each of the following completely. 1. GCF = 1 (6a) 2 (5b) 2

x( ) 9 1. GCF = 2. Grouping Number. x There is none. (9)(7) = 3. Find 2 integers whose product is 63 and sum is 5. 1, 63 3, 21 7, 9 x 2 + 5x x 3 + 5x 2 + 7x 5.

2ax (2x – 5)( ) a 3b a + 3b -30abx a( ) 2x – 5 + 3b( ) 2x – 5 (2x – 5) (2x – 5) – 5a+ 6bx– 15b 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? 6. Factor each of the following completely. 1. GCF = 1 3. The GCF = a 4. The GCF = 3b 5. The GCF = (2x – 5)

3. Find 2 integers whose product is 15 and sum is 8 1, 15 3, 5 3x GCF = 3x( ) x 2 + 8x x x x Factor each of the following completely. 3x (x )(x ) 2. Factor first term.

3c( ) 6 3c ( 6x 2 – 8xy + 15xy – 20y 2 ) 1. GCF = 2. Grouping Number. 3c 4. Split into 2 terms. (6)(-20) = 3. Find 2 integers whose product is -120 and sum is 7. -1, , 60 -3, 40 -4, 30 x 2 + 7xy – cx cxy – 60cy 2 y 2 -5, 24 -6, 20 -8, 15 8.

( ) – 4y (3x – 4y)( ) + 5y ( ) 3c ( ) 3c 5. Factor by grouping. 3c 2x 5y 2x + 5y 2x 3x 3x – 4y (3x – 4y) (3x – 4y) 6x 2 – 8xy + 15xy – 20y 2 GCF = GCF = GCF = () 2x 5y (3x – 4y) 3c( ) 6 x2x2 + 7xy – 20 y2y2 Factor each of the following completely. 18cx cxy – 60cy 2 8.

9. Factor each of the following completely. 100x 2 (10x + 7y) (10x – 7y) 1. GCF = ( ) 2 –49y 2 ( ) 2 – 1 2. Write as squares 10x7y 3. (sum)(difference)

10. Factor each of the following completely. 9 4x 2 (2x + 1) (2x – 1) 1. GCF = ( ) 2 –1 ( ) 2 – 9 2. Write as squares 2x1 3. (sum)(difference) 36x 2 –9 9 ( )

4x 2 2(2x)(-3y) = -12xy 1. GCF = 4x 2 = Not a perfect square trinomial 9y 2 = 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 (-3y) 2 -12xy ≠ -20xy 1 – 20 xy + 9y 2 Use trial and error or the grouping method Factor each of the following completely. 11.

4 4x 2 – 2xy – 18xy + 9y 2 1. GCF = 2. Grouping Number Split into 2 terms. (4)(9) = 3. Find 2 integers whose product is 36 and sum is , , -18 x2x2 – 20xy Factor each of the following completely. 11. y2y2

4x 2 (2x – y)( ) 2x -9y 2x – 9y 2x 2x – y – 9y 2x – y (2x – y) (2x – y) 5. Factor by grouping. GCF = GCF = GCF = – 2xy – 18xy + 9y 2 ( ) ( ) Factor each of the following completely x2x2 – 20xy + 9 y2y2 2x -9y (2x – y)

12. 9x Prime This not a difference of two squares. a 2 – b 2 = (a + b)(a – b) 1. GCF = Factor each of the following completely. 1

2 1. GCF = 2. Grouping Number. 1 There is none. (2)(4) = 3. Find 2 integers whose product is 8 and sum is 7. 1, 8 2, 4 x2x2 + 7x Factor each of the following completely. 13. Prime

7( ) 2 1. GCF = 2. Grouping Number. 7 There is none. (2)(7) = 3. Find 2 integers whose product is 14 and sum is , , -7 x 2 – 8x Factor each of the following completely. 14x 2 – 56x

Factor each of the following completely x 2 (8x + 1) (8x – 1) 1. GCF = ( ) 2 –1 ( ) 2 – 1 2. Write as squares 8x1 3. (sum)(difference)

4( ) Factor each of the following completely x 4 1. GCF = ( ) 2 –64 ( ) 2 – 4 2. Write as squares x (sum)(difference) x 4 16 – (x 2 + 4) (x 2 – 4) 4 (x 2 + 4) (x + 2) 4 (x – 2)

Factor each of the following completely. 6x 2 (2x – 3y)( ) 3x 5y 3x + 5y -90x 2 y 2 3x( ) 2x – 3y + 5y( ) 2x – 3y (2x – 3y) (2x – 3y) – 9xy+ 10xy– 15y 2 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? GCF = 1 3. The GCF = 3x 4. The GCF = 5y 5. The GCF = (2x – 3y)

2( ) 2( ) 3x 2 (x + 2)( ) 3x -5y 3x – 5y 1. GCF = -30xy 3x( ) x + 2 – 5y( ) x + 2 (x + 2) (x + 2) + 6x– 5xy– 10y 2. Is the product of 1 st and 4 th terms = to 2 nd and 3 rd terms? 2 3. The GCF = 3x 4. The GCF = -5y 5. The GCF = (x + 2) Factor each of the following completely x x– 10xy– 20y 2

2( ) 2 2 ( 2x 2 – 5x + 6x – 15 ) 1. GCF = 2. Grouping Number Split into 2 terms. (2)(-15) = 3. Find 2 integers whose product is -30 and sum is 1. -1, 30 -2, 13 -3, 10 -5, 6 x 2 +x – Factor each of the following completely. 4x 2 + 2x –

( ) – 5 (2x – 5)( ) + 3 ( ) 2 ( ) 2 5. Factor by grouping. 2 x 3 x + 3 x 2x 2x – 5 (2x – 5) (2x – 5) 2x 2 – 5x + 6x – 15 GCF = GCF = GCF = () x 3 (2x – 5) Factor each of the following completely. 2( ) 2 x2x2 +x – 15 4x 2 + 2x –

x 2 ( ) 3 x 2 ( 3x 2 + 4x – 15x – 20 ) 1. GCF = 2. Grouping Number. x 2 4. Split into 2 terms. (3)(-20) = 3. Find 2 integers whose product is -60 and sum is , -60 2, -30 3, -20 4, -15 x 2 – 11x – Factor each of the following completely. 3x 4 – 11x 3 – 20x 2 20.

( ) + 4 (3x + 4)( ) – 5 ( ) x 2 ( ) x 2 5. Factor by grouping. x 2 x -5 x – 5 x 3x 3x + 4 (3x + 4) (3x + 4) 3x 2 + 4x – 15x – 20 GCF = GCF = GCF = () x -5 (3x + 4) Factor each of the following completely. x 2 ( ) 3 x2x2 – 11x – 20 3x 4 – 11x 3 – 20x 2 20.

Chapter 5 Pretest