Factoring Polynomials: GCF Answers

1

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Which statement is true about the factorization of 30x2 + 40xy + 51y2?

A

The polynomial can be rewritten after factoring as 10(3x2 + 4xy + 5y2).

B

The polynomial can be rewritten as the product of a trinomial and xy.

C

The greatest common factor of the polynomial is 51x2y2.

D

The greatest common factor of the terms is 1.

2

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What is the factored form of 8x2 + 12x?

A

4(4x2 + 8x)

B

4x(2x + 3)

C

8x(x + 4)

D

8x(x2 + 4)

3

What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y?

A

5xy

B

15x3y

C

45x3y5

D

75x5y7

4

Which expression is equivalent to 10x2y + 25x2?

A

5x2(2y + 5)

B

5x2y(5 + 20y)

C

10xy(x + 15y)

D

10x2(y + 25)

5

Six equilateral triangles are connected to create a regular hexagon. The area of the hexagon is 24a2 – 18 square units. Which is an equivalent expression for the area of the hexagon based on the area of a triangle?

A

6(4a2 – 3)

B

6(8a2 – 9)

C

6a(12a – 9)

D

6a(18a – 12)

6

The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?

A

a base area of 4y square units and height of 4y2 + 4y + 12 units

B

a base area of 8y2 square units and height of y2 + 2y + 4 units

C

a base area of 12y square units and height of 4y2 + 4y + 36 units

D

a base area of 16y2 square units and height of y2 + y + 3 units

7

What is the factored form of 3x+24y?

A

3(x+8y)

B

3xy(x+8y)

C

3(3x+24y)

D

3xy(3x+24y)

8

What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?

A

7ab3

B

6a4b

C

42a5b4

D

77a8b7

9

What is the greatest common factor of 12a and 9a2?

A

9

B

36

C

3a

D

12a2

10

Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle?

A

6(10x2 + 8x + 2)

B

12(5x2 + 4x + 2)

C

6x(10x2 + 8x + 2)

D

12x(5x2 + 4x + 2)

11

What is the greatest common factor of 24s3, 12s4, and 18s?

A

3

B

6

C

3s

D

6s

12

What is the factored form of 3x+24y?

A

3(x+8y)

B

3xy(x+8y)

C

3(3x+24y)

D

3xy(3x+24y)

13

What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y?

A

5xy

B

15x3y

C

45x3y5

D

75x5y7

14

Which statement is true about the factorization of 30x2 + 40xy + 51y2?

A

The polynomial can be rewritten after factoring as 10(3x2 + 4xy + 5y2).

B

The polynomial can be rewritten as the product of a trinomial and xy.

C

The greatest common factor of the polynomial is 51x2y2.

D

The greatest common factor of the terms is 1.

15

What is the greatest common factor of 4k, 18k4, and 12?

A

2

B

4

C

2k

D

4k

16

Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars. Which expression represents her gross pay each day?

A

5h+8

B

8h+5

C

7h+11.2

D

11.2h+7

17

What is the completely factored form of the expression 16x2 + 8x + 32?

A

4(4x2 + 2x + 8)

B

4(12x2 + 4x + 28)

C

8(2x2 + x + 4)

D

8x(8x2 + x + 24)

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