Free Printable Factoring by Removing the GCF

1.

What is the greatest common factor of 20a²b² and 50b³?

a)

100a²b²

b)

10b³

c)

10ab²

d)

10b²

2.

Factor the polynomial by removing the GCF:

2x + 18

a)

2(x + 9)

b)

2(x + 8)

c)

2(2x + 9)

d)

cannot be factored

3.

Factor the polynomial by removing the GCF:

x² - 5x

a)

1(x - 5)

b)

x(x - 5x)

c)

x(x - 5)

d)

x²(1 - 5)

4.

Factor the polynomial by removing the GCF:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

5.

Factor the polynomial by removing the GCF:

10x³ - 15x

a)

x(10x² - 15)

b)

5x(2x² - 3)

c)

5(2x³ - 3x)

d)

5x²(10x - 3)

6.

What is the GCF of the binomial shown below?

24x³ + 36x²

a)

8x

b)

6x²

c)

12x²

d)

4x

e)

12x³

7.

What is the GCF of the binomial shown below?

72y⁵ + 18y²

a)

y²

b)

4y⁵

c)

18y

d)

18y²

e)

9y²

8.

Factor the polynomial by removing the GCF

4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

9.

What is the greatest common factor of the three terms in the expression?
24m³n⁵p + 6mn⁴p² + 4mn⁵

a)

2mn

b)

24mn⁴

c)

2mn⁴

d)

2mn⁴p

10.

Factor the GCF
39y⁵ + 12y⁴- 3y³

a)

3y(13y⁴ + 4y³ - y²)

b)

3y³(13y² + 4y - 1)

c)

y³(39y² + 12y - 3)

d)

not factorable

11.

Factor:
$a^2b^2+a$

a)

$a^2\left(b^2+1\right)$

b)

$ab\left(ab+1\right)$

c)

$a\left(ab^2+1\right)$

d)

$a\left(b^2+1\right)$

12.

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)

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

13.

Factor:

9xz^3+18yz^2+24z^2

a)

$3z^2\left(3xz+6y+8\right)$

b)

$9z^2\left(xz+2y+3\right)$

c)

$3z\left(3xz^2+6yz+24z\right)$

d)

$9z\left(xz^2+2yz+3z\right)$

14.

Factor:

16x^6y+16x^2y^4+32x^3y^2

a)

$16x^2y\left(x^3+y^4+2xy\right)$

b)

$16xy\left(x^6+xy^3+2x^2y\right)$

c)

$16x^2y\left(x^4+y^3+2xy\right)$

d)

$16x^2y\left(x^4+y^3+2\right)$

15.

The following are examples of quadratic trinomials EXCEPT:

a)

x^2+2y+1

b)

$3a-2a+4$

c)

$2y^2+x-4$

d)

$z^2-5z+6$

16.

Factor

k^2+7k+10

.

a)

$(k+2)(k-5)$

b)

$(k+2)(k+5)$

c)

$(k+10)(k+4)$

d)

$(k-2)(k-5)$

17.

Factor $k^2-2k-24$

a)

$(k-4)(k+6)$

b)

$(k+4)(k+6)$

c)

$(k+6)(k-1)$

d)

$(k+4)(k-6)$

18.

Factor the expression: 10v² + 11v - 8

a)

(5v + 8)(2v + 1)

b)

(v + 8)(v - 1)

c)

(5v + 8)(2v - 1)

d)

(10v - 8)(v + 1)

19.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

20.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

21.

$Factor\ 3n^2-8n+4$
Type in answer with no spaces

[e.g. (n+?)(n-?)]

(a)

22.

$Factor\ 5n^2+19n+12$
Type in answer with no spaces

[e.g. (n+?)(n-?)]

(a)

23.

$Factor\ 2n^2+11n+5$
Type in answer with no spaces

[e.g. (n+?)(n-?)]

(a)

24.

$Factor\ 7n^2+53n+28$
Type in answer with no spaces

[e.g. (n+?)(n-?)]

(a)

Factoring by Removing the GCF

Total questions: 24

Worksheet time: 46mins

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