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Difference of squares, GCF and a few trinomials

Total questions: 40

Worksheet time: 4hrs 7mins

Name
Class
Date
1.
Factor out the GCF:
12x + 6
a)
6(2x + 1)
b)
3(4x + 2)
c)
6x(2x + 1)
d)
2(6x + 3)
2.
Factor out the GCF:
10x³ - 15x
a)
x(10x² - 15)
b)
5x(2x² - 3)
c)
5(2x³ - 3x)
d)
5x²(10x - 3)
3.

Factor 4b5+4b3+16b2

a)

4b3(b4+b2+4b)

b)

4b3(b4+4b+5)

c)

4(b5+b3+4b2)

d)

4b2(b3+b+4)

4.
Factor
10x2 + 15x-5
a)
25(10x3+45x-15)
b)
5(2x3 + 3x2-x)
c)
x(10x3+15x-5)
d)
5(2x2+3x-1)
5.
Factor:x2 - 25
a)
( x + 5 ) ( x - 5 ) 
b)
( x - 5 ) ( x - 5 ) 
c)
( x + 5 ) ( x + 5 ) 
d)
Prime
6.
Factor out the GCF:
10x³ - 15x
a)
x(10x² - 15)
b)
5x(2x² - 3)
c)
5(2x³ - 3x)
d)
5x²(10x - 3)
7.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

8.

Factor 4x2-9

a)

(4x-9)(4x+9)

b)

(2x-3)(2x+3)

c)

2x-3

d)

(2x-4.5)(2x+4.5)

9.
Fully Factor the Following
25x2-81
a)
(5x-9)2
b)
(5x+9)(5x-9)
c)
25(x-9)2
d)
(9x+5)(9x-5)
10.
3x2 - 75
a)
3( x + 5 ) ( x - 5 ) 
b)
Prime
c)
( x + 5 ) ( x - 5 ) 
d)
3( x - 5 ) ( x - 5 ) 
11.
9n2 + 1
a)
(3n + 1) (3n - 1)
b)
(3n - 1) (3n - 1)
c)
(n + 3) (n - 3)
d)
Can't factor using Diff. of Squares
12.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
13.
Factor:
2n3+16n+12
a)
2n(n3+24n+6)
b)
2(n3+8n+6)
c)
2n(n3+8n+6)
d)
3(n3+8n+6)
14.
Factor
81m2 - 1 
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
15.
   6m2 + 16m
a)
2(3m2 + 8m)
b)
2m(3m + 8)
c)
2m(3m - 8m)
d)
not factorable
16.
Factor:
p2 - 14p
a)
p(1 - 14)
b)
2p(p - 7)
c)
p2(1-14)
d)
p(p - 14)
17.
Factor:
x2 - 49
a)
(x + 7)(x - 7)
b)
(x + 7)2
c)
(x - 7)2
d)
(x+7)(x-1)
18.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
19.

We can't factor using difference of two square this

25x2 - 51y2. Why?

a)

Because 51 is not a perfect cubed number.

b)

Because 51 is not a perfect squared number.

c)

Because 25 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

20.

We can't factor using difference of two square this

49x2 + 4y2. Why?

a)

Because 4 is not a perfect cubed number.

b)

Because 4 is not a perfect squared number.

c)

Because 49 is not a perfect squared number.

d)

Because we can't factor using difference of two squares if it is addition sign.

21.

4x2 - 16

a)

4(2x + 4) (x - 2)

b)

4(4x + 2) (x - 2)

c)

(2x + 4) (2x - 4)

d)

4(x + 2) (x - 2)

22.

x2 - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)2

d)

x + 4(x - 4)

23.
4m2 + 49
a)
(2m + 7) (2m - 7)
b)
(2m - 7) (2m - 7)
c)
(m + 7) (m - 7)
d)
Can't factor using Diff. of Squares
24.
4a2 - 25
a)
(2a + 5) (2a - 5)
b)
(2a - 5) (2a - 5)
c)
(x + 5) (x - 5)
d)
Can't factor using Diff. of Squares
25.
q2 - 121
a)
(q + 11) (q - 11)
b)
(q - 11) (q - 11)
c)
(q + 11) (q + 11)
d)
Can't factor using Diff. of Squares
26.

x2 - 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Unfactorable

27.
Factor:
56a3-8a
a)
8a2(56a3-8a)
b)
8a(7a2-1)
c)
8a(7a3-a)
d)
8a2(35a2-a)
28.
Factor:
 2n2-8n3
a)
2n2(n-4n2)
b)
2n2(1-4n)
c)
2n3(10-8n2)
d)
3n(1-4n)
29.
Factor:
2n3+16n+12
a)
2n(n3+24n+6)
b)
2(n3+8n+6)
c)
2n(n3+8n+6)
d)
3(n3+8n+6)
30.
factor:x2 - 25
a)
( x + 5 ) ( x - 5 ) 
b)
( x - 5 ) ( x - 5 ) 
c)
( x + 5 ) ( x + 5 ) 
d)
Prime
31.
Factor
81m2 - 1 
a)
not factorable
b)
(m-9)(m+9)
c)
9m(9m-1)
d)
(9m-1)(9m+1)
32.
12x + 9
a)
3(4x + 3)
b)
x(12+9)
c)
3(4x - 3)
d)
not factorable
33.
   6m2 + 16m
a)
2(3m2 + 8m)
b)
2m(3m + 8)
c)
2m(3m - 8m)
d)
not factorable
34.
Factor:
p2 - 14p
a)
p(1 - 14)
b)
2p(p - 7)
c)
p2(1-14)
d)
p(p - 14)
35.
Factor completely: 
3x2 + 18x +15
Hint: Factor GCF first.
a)
3(x2 + 6x + 5)
b)
(x + 5)(x + 1)
c)
3(x + 5)(x + 1)
d)
Prime
36.

What method should you use to factor the polynomial?

x2 - 36

a)

Factor by Grouping

b)

Factor out the GCF

c)

Difference of Squares

d)

Difference of 2 Cubes

37.

What is ALWAYS the first step when factoring?

a)

Look for the GCF

b)

Write a, b, and c

c)

Difference of squares

d)

Group

38.

Factor using GCF:  28c−1228c-12  



(a)  

39.

Factor using the GCF:   10m2n+30mn2+5mn\ \ 10m^2n+30mn^2+5mn  



(a)  

40.

Factor using the difference of squares. **Always check for a GCF first**       x2−225x^2-225  



(a)  

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