Free Printable Algebra Essentials: Factoring out a GCF

1.

Factor out the GCF

3x³ + 9x

a)

3x (x²+ 3)

b)

3x ( x³ + 9)

c)

x (3x² + 9)

d)

3x (x³ + 3x)

2.

Find the factors

16xy - 24y

a)

4y (4x - 6)

b)

8y (2xy - 3y)

c)

8y (2x - 3)

d)

2xy (8 - 12y)

3.

9xyz + 3xy

a)

xy (9z + 3)

b)

9xy (z + 3)

c)

3xy (3xyz + 1)

d)

3xy (3z + 1)

4.

Factor using GCF or monomial factoring:

2n²- 8n³

a)

2n²(n - 4n²)

b)

2n²(1 - 4n)

c)

2n³(10 - 8n²)

d)

3n(1 - 4n)

5.

What is the GCF?

5x²+ 20x

a)

5

b)

x

c)

5x

d)

20x

6.

What is the GCF?

3x²- 2x

a)

3

b)

3x

c)

x

d)

2

7.

What is the GCF? 2x²-4x+8

a)

2x

b)

2

c)

x

d)

1

8.

Factor:
10x + 15

a)

100x + 150

b)

10(x + 5)

c)

1(10x + 15)

d)

5(2x + 3)

9.

Factor:
x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

10.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

11.

Factor:

7x+49

a)

$7x\left(x+49\right)$

b)

$7\left(x+7\right)$

c)

$49\left(x+7\right)$

d)

$x\left(7+49\right)$

12.

Factor:
$5a^2-15$

a)

$5\left(a^2-15\right)$

b)

$5a\left(a-15\right)$

c)

$5\left(a^2-3\right)$

d)

$5a\left(a-3\right)$

13.

$12c^2-20a^2$

Factor:

a)

$2\left(6c^2-10a^2\right)$

b)

$4\left(3c^2-5a^2\right)$

c)

$2a^2c^2\left(6-10\right)$

d)

$4\left(ca\right)^2\left(3-5\right)$

14.

$36a^2+24a$

Factor:

a)

$12a\left(3a+2\right)$

b)

$a\left(36a+24\right)$

c)

$12\left(3a^2+2a\right)$

d)

$a^2\left(36+24a\right)$

15.

Factor:
$18x^4-12x^2$

a)

$6x^2\left(3x^2-2\right)$

b)

$x^2\left(18x^2-12\right)$

c)

$6\left(3x^2-2x^2\right)$

d)

$6x\left(2x^3-2x\right)$

16.

Factor:

12ab^3+20b

a)

$4ab\left(3b+5\right)$

b)

$b\left(12ab^2+20\right)$

c)

$4b\left(3ab^2+5\right)$

d)

$12b\left(ab^2+2\right)$

17.

Factor:
$8ab-56a$

a)

$8a\left(b-7\right)$

b)

$8\left(ab-7a\right)$

c)

$a\left(8b-56\right)$

d)

$8ab\left(1-7b\right)$

18.

Factor:
$15xy+30x^2y^2$

a)

$xy\left(15+30xy\right)$

b)

$15\left(xy+2x^2y^2\right)$

c)

$15xy\left(1+2xy\right)$

d)

$5xy\left(3+6xy\right)$

19.

Factor using GCF or monomial factoring:

2x + 18

a)

2(x + 9)

b)

2(x + 8)

c)

2(2x + 9)

d)

cannot be factored

20.

Factor using GCF or monomial factoring:

w³ + 3w

a)

3w(1)

b)

w(w² + 3)

c)

w³(w + 3)

21.

Factor by using GCF:

8r³ + 16r²

a)

4r²(2r + 4)

b)

8r²(r + 2)

c)

8(r³ + r²)

d)

4(r³ + 2r²)

22.

Factor by using GCF:

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

Prime

23.

Factor using GCF

16x² - 20xy

a)

4 (4x² - 5xy)

b)

4x (4x - 5y)

c)

4x² (4 - 5y)

d)

2(duck)

24.

Factor by GCF:

18a²-15a

a)

15a(3a-1)

b)

3a(6a-1)

c)

3(6a-5)

d)

3a(6a-5)

25.

GCF 24 and 36

a)

8

b)

6

c)

12

d)

4

26.

GCF of 12 and 18

a)

3

b)

4

c)

6

d)

2

27.

What is the GCF? 3x²-2x

a)

3

b)

3x

c)

x

d)

2

28.

What is the GCF of this polynomial: $10x^3+15x^{5\ }$

a)

$5x^2$

b)

$5x^3$

c)

$10x$

d)

$10x^3$

29.

Factor 24x - 64 using the GCF

a)

12 (2x - 5)

b)

6 (4x - 12)

c)

8 (3x - 8)

d)

24 (x - 3)

30.

Can 5x + 33 be factored

a)

yes

b)

no

31.

Factor by GCF:

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

Prime

32.

Factor
4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

33.

Factor:
10a⁴+16a+10a²

a)

2a(5a³⁺8+5a)

b)

2a⁴(5a+8a²+5a³)

c)

2a⁴(10+16a+40a²)

d)

3a³(5+8a+a²)

34.

Factor:
2n³+16n+12

a)

2n(n³+24n+6)

b)

2(n³+8n+6)

c)

2n(n³+8n+6)

d)

3(n³+8n+6)

35.

Factor out the GCF: $5x^2+15x^3$

a)

$5x^2\left(1+3x\right)$

b)

$5x\left(x+3x^2\right)$

c)

$5\left(x^2+3x^3\right)$

36.

Factor out the GCF: $3x^2+6x^3$

a)

$3x^2\left(1+2x\right)$

b)

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

c)

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

37.

Factor out the GCF: $4x^2+10x^3$

a)

$2x^2\left(2+5x\right)$

b)

$2x\left(2x+5x^2\right)$

c)

$2\left(2x^2+5x^3\right)$

38.

Factor out the GCF: $x^2+x^3$

a)

$x^2\left(1+x\right)$

b)

$x\left(x+x^2\right)$

c)

$1\left(x^2+x^3\right)$

39.

Factor out the GCF: $7x^4+14x^2$

a)

$7x^2\left(x^2+2\right)$

b)

$7x\left(x^3+2x\right)$

c)

$7\left(x^4+2x^2\right)$

40.

Factor out the GCF: $9x+36$

a)

$9\left(x+4\right)$

b)

$3\left(3x+12\right)$

c)

$9\left(x+36\right)$

Algebra Essentials: Factoring out a GCF

Total questions: 40

Worksheet time: 1hrs 15mins

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