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Worksheets

Alg 2 GCF

Total questions: 33

Worksheet time: 3hrs 45mins

Name
Class
Date
1.

What is the greatest common factor of 8x2 and 4x?

a)

8x2

b)

4x2

c)

2x

d)

4x

2.

What is the greatest common factor of 18xy3 and 25x3y2?

a)

xy2

b)

x3y2

c)

1

d)

x2y3

3.

Factor:

2n2-8n3

a)

2n2(n-4n2)

b)

2n2(1-4n1)

c)

2n3(10-8n2)

d)

3n(1-4n)

4.
Factor:
18a2-15a
a)
15a(3a-1)
b)
3a(6a-1)
c)
3(6a-5)
d)
3a(6a-5)
5.
Factor
12x + 9
a)
3(4x + 3)
b)
x(12+9)
c)
3(4x - 3)
d)
not factorable
6.

2x + 4

a)

2(x + 2)

b)

2(x + 4)

c)

4(x + 4)

d)

4(x + 2)

7.

15x4 + 20x3 - 25x

a)

5x2(3x2 + 4x - 5)

b)

5x(3x3 + 4x2 - 5x)

c)

5x(3x3 + 4x2 - 5)

d)

5(3x4 + 4x3 - 5x)

8.

6x2y - 18xy2

a)

6(x - 3y)

b)

6xy(x - 3y)

c)

6xy2(x - 3)

d)

6x2y(3y - 1)

9.

24x2 + 30

a)

6(4x2 + 5)

b)

6x(4x + 5)

c)

2(12x2 + 15)

d)

2x(12x + 15)

10.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
11.
Factor:
2n3+16n+12
a)
2n(n3+24n+6)
b)
2(n3+8n+6)
c)
2n(n3+8n+6)
d)
3(n3+8n+6)
12.
What is the GCF of 18k and 15k3
a)
3k2
b)
3k3
c)
3k
d)
5k
13.
Factor:
10x + 15
a)
100x + 150
b)
10(x + 5)
c)
1(10x + 15)
d)
5(2x + 3)
14.
Factor:
x2 - 5x
a)
1(x - 5)
b)
x(x - 5x)
c)
x(x - 5)
d)
x2(1 - 5)
15.

Factor 7x + 21 using the GCF

a)

7(x+3)

b)

7x + 3

c)

3(x + 7)

d)

x(7 + 3)

16.

Factor the polynomial.

  6x2−9x+96x^2-9x+9  

a)

   3x(2x−3x+3)3x\left(2x-3x+3\right)  

b)

   3(2x2+3x+3)3\left(2x^2+3x+3\right)  

c)

   3x(3x2−6x+6)3x\left(3x^2-6x+6\right)  

d)

   3(2x2−3x+3)3\left(2x^2-3x+3\right)  

17.

Factor the following binomial (GCF):

36a2+24a36a^2+24a  

a)

12a(3a+2)12a\left(3a+2\right)  

b)

a(36a+24)a\left(36a+24\right)  

c)

12(3a2+2a)12\left(3a^2+2a\right)  

d)

a2(36+24a)a^2\left(36+24a\right)  

18.
What is the GCF of 18k and 15k3
a)
3k2
b)
3k3
c)
3k
d)
5k
19.
GCF of 35f + 40f
a)
5f
b)
10
c)
f
d)
2f
20.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
21.

Factor completely


18x3 + 81x - 27

a)

9x (2x2 + 9x - 3)

b)

3 (6x3 + 27x - 9)

c)

9 (2x3 + 9x - 3)

d)

9 (2x2 + 9x - 3)

22.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
23.
Factor
4b5+4b3+16b2
a)
4b3(b4+b2+4b)
b)
4b3(b4+4b+5)
c)
4(b5+b3+4b2)
d)
4b2(b3+b+4)
24.

What is the GCF of 10a2b3 and 20a2b2?

a)

20a2b3

b)

10a2b3

c)

20ab2

d)

10a2b2

25.

Factor

5ab2c11 + 2bc5

a)

bc5(5ab2c6 + 2b)

b)

bc5(5abc6 + 2)

c)

b2c5(5bc6 + 2)

d)

c4(5a2b2c7 + 2bc)

26.

Factor:

80x5-70x2-60x7

a)

2x2(80x3-70-60x6)

b)

10x2(80x4-70x-60x6)

c)

10x2(8x3-7-6x5)

d)

3x2(80x3-40-60x5)

27.

Factor by using GCF:

10x2 + 15x-5

a)

25(10x3+45x-15)

b)

5(2x3 + 3x2-x)

c)

x(10x3+15x-5)

d)

5(2x2+3x-1)

28.

Factor:

56a3-8a

a)

8a2(56a3-8a)

b)

8a(7a2-1)

c)

8a(7a3-a)

d)

8a2(35a2-a)

29.

Factor

12j2k3 - 20hj

a)

4j(3jk3 - 5h)

b)

4j(6jk3 - 10h)

c)

4j(3jk2 - 5h)

d)

4j2(24j2k3 - 20h)

30.

What is the greatest common factor of the three terms in the expression

-96xy - 144x - 84

a)

12x

b)

-12

c)

-12xy

d)

12

31.

Factor the polynomial.

5x+60x45x+60x^4  

a)

5x(1+12x3)5x\left(1+12x^3\right)  

b)

5x(12x4)5x\left(12x^4\right)  

c)

5x5(x+12)5x^5\left(x+12\right)  

d)

5x(1+12x4)5x\left(1+12x^4\right)  

32.

Factor the polynomial.

12x5+16x312x^5+16x^3   

a)

  4x3(3x5+4x)4x^3\left(3x^5+4x\right)  

b)

  2x3(6x2+8)2x^3\left(6x^2+8\right)  

c)

  4x3(3x2+4)4x^3\left(3x^2+4\right)  

d)

  6x(2x4+3x2)6x\left(2x^4+3x^2\right)  

33.

Factor the polynomial.

  6x2−9x+96x^2-9x+9  

a)

   3x(2x−3x+3)3x\left(2x-3x+3\right)  

b)

   3(2x2+3x+3)3\left(2x^2+3x+3\right)  

c)

   3x(3x2−6x+6)3x\left(3x^2-6x+6\right)  

d)

   3(2x2−3x+3)3\left(2x^2-3x+3\right)