Factoring Polynomials: GCF Answers

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Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two options.

A
2
B
4xy
C
12x
D
24
E
44y
2
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What is the factored form of 3x+24y?

A
3(x+8y)
B
3xy(x+8y)
C
3(3x+24y)
D
3xy(3x+24y)
3

Which expression is equivalent to 10x2y + 25x2?

A
5x2(2y + 5)
B
5x2y(5 + 20y)
C
10xy(x + 15y)
D
10x2(y + 25)
4

What is the fully factored form of 32a3 + 12a2?

A
4a2(8a + 3)
B
4a(8a2 + 3a)
C
12a2(3a + 1)
D
12a(3a2 + a)
5

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.
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

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
8

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

A
4(4x2 + 8x)
B
4x(2x + 3)
C
8x(x + 4)
D
8x(x2 + 4)
9

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

A
5xy
B
15x3y
C
45x3y5
D
75x5y7
10

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

A
7ab3
B
6a4b
C
42a5b4
D
77a8b7

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Factoring Polynomials: GCF Answers — Summer 2026…