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Worksheets

Factoring by GCF

Total questions: 31

Worksheet time: 53mins

Name
Class
Date
1.

Factor:

16a +4b

a)

4(4a+b)

b)

2(8a+2b)

2.

Factor:

9x2 + 36x

a)

9 (x2 + 4x)

b)

9x (x + 4)

c)

x( 9x +36)

3.

Factor:

7x2 +35xy

a)

x (7x + 35y)

b)

7 (x2 + 35xy)

c)

7x (x + 5y)

4.

Factor:

3n2 + 6n

a)

3 (n2 + 6n)

b)

3n (n + 2)

c)

n (3n + 6)

5.

Factor:

5d2e - 35de2

a)

5 (d2e - 7de2)

b)

5d (de - 7e2)

c)

5de (d - 7e)

d)

5e (d2 - 7e)

6.

Factor:

3m4n3 + 15m2n3

a)

3mn (m3n2 + 5mn2)

b)

3m2n3 (m2 + 5 )

c)

3m2n3 (m + 5)

7.

Factor:

a5b - a3

a)

a3 (a2b -1)

b)

a3 (a2 b)

c)

a(a4b - a2)

8.

Factor:

15x2y2 + 25xy + x

a)

5xy (xy + 5)

b)

x (15xy2 + 25y + 0)

c)

x(15xy2 + 25y +1)

d)

5x (3xy2 +5y +1)

9.

Factor:

18c3d4 - 27c2d2 + 36cd

a)

3cd (6c2d3 - 9cd + 12)

b)

9cd (2c2d3 - 3cd + 4)

c)

3 (6c3d4 - 9c2d2 +12cd)

d)

9(2c3d4 - 3c2d2 +4 cd

10.

Factor:

3p2q - 9pq2 -24pq

a)

3 (p2q - 3pq2 -8pq)

b)

3pq (-3q - 8)

c)

3pq (p - 3q -8)

11.

Factor:

4r2 + 8r2s +28r4

a)

4r2 ( 1 + 2s +7r2)

b)

4r2 (2s + 7r2)

c)

2r2 (2 +4s + 14r2 )

12.

Factor:

15x2y2 +25xy -30x

a)

5xy (3xy + 5y - 6)

b)

5x (3xy2 +5y - 6)

c)

5x (3xy + 5y - 6)

13.

Factor:

10m2y +20my2 - 5my

a)

5 (2m2y + 4my2 - my)

b)

5my (2m + 4y)

c)

5my (2m + 4y -1)

14.

Factor:

2n2-8n3

a)

2n2(n-4n2)

b)

2n2(1-4n2)

c)

2n3(10-8n2)

d)

3n(1-4n)

15.

Factor:

2n3+16n+12

a)

2n(n3+24n+6)

b)

2(n3+8n+6)

c)

2n(n3+8n+6)

d)

3(n3+8n+6)

16.

Factor:

10a4+16a+10a2

a)

2a(5a3+8+5a)

b)

2a4(5a+8a2+5a3)

c)

2a4(10+16a+40a2)

d)

3a3(5+8a+a2)

17.

Factor:

39y5 + 12y4 - 3y3

a)

3y(13y4 + 4y3 - y2)

b)

3y3(13y2 + 4y - 1)

c)

y3(39y2 + 12y - 3)

18.

Factor:

80x5-70x2-60x7

a)

2x2(80x3-70-60x6)

b)

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

c)

10x2(8x3-7-6x5)

d)

3x2(80x3-40-60x5)

19.

Factor:

24c5 - 12c3

a)

6(4c5 - 2c3)

b)

12c3(2c2)

c)

12c3(2c2 - 1)

d)

12c3(2c2 - 0)

20.

Factor:

36a5bc - 12c

a)

12c (3a5b - 1)

b)

6c (6a5b - 2)

c)

12c (3a5b - c)

d)

12abc(3a4 - 1)

21.

Factor:


21x7y6 + 30x5y8 - 18x5y6

a)

3xy (7x4y2 + 10x2y6 - 6x)

b)

3x5y6 (7y2 + 10 x2 - 6)

c)

3x5y6 (7x2 + 10y2 - 6)

d)

3x7y8 (7y2 + 10x2 - 6x2y2)

22.

Factor:


4a3b5 - 18a2b3 + 8a3b3

a)

4a2b3 (ab2 - 4 + 2a)

b)

2a2b3 (2ab2 - 9 + 4a)

c)

2a2b3 (2ab - 9ab + 4)

d)

a2b (4ab - 18a2b3 + 8ab2)

23.

Factor using the GCF

 28a4b6+42a3b328a^4b^6+42a^3b^3 

a)

 7ab7ab  

b)

 7a3b37a^3b^3  

c)

 7ab(4a3b5+6a2b2)7ab\left(4a^3b^5+6a^2b^2\right)  

d)

 7a3b3(4ab3+6)7a^3b^3\left(4ab^3+6\right)  

24.

Factor:


12x2y4 - 6xy

a)

3xy (4xy3 - 2)

b)

6xy (2xy3 - 1)

c)

6xy (2x3y5 - x2y2)

d)

6xy ( 2xy3)

25.

Factor the GCF out of the expression.

 6e3f11ef6e^3f-11ef  

a)

 ef(6e211)ef\left(6e^2-11\right)  

b)

 6ef(e22)6ef\left(e^2-2\right)  

c)

 ef(6e2f11ef)ef\left(6e^2f-11ef\right)  

26.

Factor the GCF out of the expression.

 28b314b2+42b28b^3-14b^2+42b  

a)

 14b(2b2b+3)14b\left(2b^2-b+3\right)  

b)

 7b(4b22b+6)7b\left(4b^2-2b+6\right)  

c)

 14(2b3b2+3b)14\left(2b^3-b^2+3b\right)  

27.

Factor the GCF out of the expression.

 2d2e28d6e62d^2e^2-8d^6e^6  

a)

 2d2e2(14d4e4)2d^2e^2\left(1-4d^4e^4\right)  

b)

 2(d2e24d6e6)2\left(d^2e^2-4d^6e^6\right)  

c)

 2d2e2(18d3e3)2d^2e^2\left(1-8d^3e^3\right)  

28.
Factor by GCF:
17xy - x
a)
17(xy - x)
b)
y(17x - x)
c)
x(17y - 1)
d)
not factorable
29.

Factor:
5t8+7t6+2t25t^8+7t^6+2t^2

a)

t(5t7+7t5+2t)t\left(5t^7+7t^5+2t\right)

b)

t2(5t6+7t4+2)t^2\left(5t^6+7t^4+2\right)

c)

Prime

d)

5t2(t6+7t4+2t)5t^2\left(t^6+7t^4+2t\right)

30.


Factor:
7a221a+357a^2-21a+35

a)

7(a221a+35)7\left(a^2-21a+35\right)

b)

7(a23a+5)7\left(a^2-3a+5\right)

c)

7a(a23a+5)7a\left(a^2-3a+5\right)

d)

7a(a3+5)7a\left(a-3+5\right)

31.

Factor:

9x7y53x2y69x^7y^5-3x^2y^6

a)

3(3x7y5x2y6)3\left(3x^7y^5-x^2y^6\right)

b)

3xy(3x6y4xy5)3xy\left(3x^6y^4-xy^5\right)

c)

3x2y(3x5y4y5)3x^2y\left(3x^5y^4-y^5\right)

d)

3x2y5(3x5y)3x^2y^5\left(3x^5-y\right)