Chapter 5

Pretest

Factor each of the following completely.

1. 20

5xy2( )

5 5

x6 – 34

1. GCF = 5x7y2 – 15x y2 x y2

xy2 xy2

3. Find 2 integers whose product is 10

and sum is 7

1, 10

2, 5

(x )(x )+ 2 + 5

1. GCF = 2. x2 + 7x + 10

Factor each of the following completely.

1

2. Factor first term.

Factor each of the following completely.

3( )

2

3(2x2 + x + 4x + 2 )

1. GCF =

2. Grouping Number.

3

4. Split into 2 terms.

(2)(2) =

3. Find 2 integers whose product is 4 and sum is 5.

1, 4

x2 + 5x + 2

4

6x2 + 15x + 63.

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)

2x2 + x + 4x + 2

GCF =

GCF =

GCF =

( )

x

2

(2x + 1)

3( )

2x2 + 5x + 2

6x2 + 15x + 63.

2(6a)(5b) = 60ab

36a2 =

(6a + 5b)2

25b2 =

2. Are the 1st and 3rd terms are perfect squares

√

3. Is 2nd term double the product of the values whose squares

are the 1st and 3rd terms

√

4. 36a2 + 60ab + 25b2

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

x2 + 5x + 763

Factor each of the following completely.

9x3 + 5x2 + 7x5.

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 1st and 4th terms = to 2nd and 3rd 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 + 3 + 5

1. GCF =

3x( )x2 + 8x + 15

7. 3x3 + 24x2 + 45x

Factor each of the following completely.

3x

(x )(x )

2. Factor first term.

3c( )6

3c(6x2 – 8xy + 15xy – 20y2)

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, 120

-2, 60

-3, 40

-4, 30

x2 + 7xy – 20-120

Factor each of the following completely.

18cx2 + 21cxy – 60cy2

y2

-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)

6x2 – 8xy + 15xy – 20y2

GCF =

GCF =

GCF =

( )

2x

5y

(3x – 4y)

3c( )6x2 + 7xy – 20y2

Factor each of the following completely.

18cx2 + 21cxy – 60cy28.

9.

Factor each of the following completely.

100x2

(10x + 7y)(10x – 7y)

1. GCF =

( )2

– 49y2

( )2–

1

2. Write as squares10x 7y

3. (sum)(difference)

10.

Factor each of the following completely.

9 4x2

(2x + 1)(2x – 1)

1. GCF =

( )2

– 1

( )2–

9

2. Write as squares

2x 13. (sum)(difference)

36x2 – 9

9

( )

4x2

2(2x)(-3y) = -12xy

1. GCF =

4x2 =

Not a perfect square trinomial

9y2 =

2. Are the 1st and 3rd terms perfect squares

3. Is 2nd term double the product of the values whose squares are the 1st and 3rd terms

√(2x)2

(-3y)2

-12xy ≠ -20xy

1– 20xy + 9y2

Use trial and error or

the grouping method

Factor each of the following completely.

11.

4

4x2 – 2xy – 18xy + 9y2

1. GCF =

2. Grouping Number.

1

4. Split into 2 terms.

(4)(9) =

3. Find 2 integers whose product is 36 and sum is -20.

-1, -36

-2, -18

x2 – 20xy + 9

36

Factor each of the following completely.

11. y2

4x2

(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 + 9y2

( ) ( )

Factor each of the following completely.

11. 4x2 – 20xy + 9y2

2x

-9y

(2x – y)

12. 9x2 + 49

PrimeThis not a difference of two

squares.a2 – b2 = (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

x2 + 7x + 4

8

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 -8.

-1, -14

-2, -7

x2 – 8x + 714

Factor each of the following completely.

14x2 – 56x + 4914.

Factor each of the following completely.

15. 64x2

(8x + 1)(8x – 1)

1. GCF =

( )2

– 1

( )2–

1

2. Write as squares8x 1

3. (sum)(difference)

4( )

Factor each of the following completely.

16. 4x4 1. GCF =

( )2

– 64

( )2–

4

2. Write as squares

x2 43. (sum)(difference)

x4 16–

(x2 + 4)(x2 – 4)4

(x2 + 4)(x + 2)4 (x – 2)

Factor each of the following completely.

6x2

(2x – 3y)( )

3x 5y

3x + 5y

-90x2y2 3x( )2x – 3y + 5y( )2x – 3y

(2x – 3y) (2x – 3y)

– 9xy + 10xy – 15y2

2. Is the product of 1st and 4th terms = to 2nd and 3rd terms?

17. 1. GCF = 1

3. The GCF = 3x

4. The GCF = 5y

5. The GCF = (2x – 3y)

2( )

2( )3x2

(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 1st and 4th terms = to 2nd and 3rd terms?

2

3. The GCF = 3x

4. The GCF = -5y

5. The GCF = (x + 2)

Factor each of the following completely.

18. 6x2 + 12x – 10xy– 20y

2

2( )2

2(2x2 – 5x + 6x – 15)

1. GCF =

2. Grouping Number.

2

4. 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

x2 + x – 15-30

Factor each of the following completely.

4x2 + 2x – 3019.

1

( )– 5

(2x – 5)( )

+ 3( )

2( )

2

5. Factor by grouping.

2

x 3

x + 3

x 2x 2x – 5(2x – 5) (2x – 5)

2x2 – 5x + 6x – 15

GCF =

GCF =

GCF =

( )

x

3

(2x – 5)

Factor each of the following completely.

2( )2x2 + x – 15 4x2 + 2x – 3019.

x2( )3

x2(3x2 + 4x – 15x – 20)

1. GCF =

2. Grouping Number.

x2

4. Split into 2 terms.

(3)(-20) =

3. Find 2 integers whose product is -60 and sum is -11.

1, -60

2, -30

3, -20

4, -15

x2 – 11x – 20-60

Factor each of the following completely.

3x4 – 11x3 – 20x220.

( )+ 4

(3x + 4)( )

– 5( )

x2( )

x2

5. Factor by grouping.

x2

x -5

x – 5

x 3x 3x + 4(3x + 4) (3x + 4)

3x2 + 4x – 15x – 20

GCF =

GCF =

GCF =

( )

x

-5

(3x + 4)

Factor each of the following completely.

x2( )3x2 – 11x – 20 3x4 – 11x3 – 20x220.

Chapter 5

Pretest