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Factoring Review

Total questions: 37

Worksheet time: 2hrs 42mins

Name
Class
Date
1.

When we factor a polynomial, the first thing we look for is any (a)  

2.
GCF of 24 and 56
a)
2
b)
4
c)
6
d)
8
3.
GCF of 12 and 18
a)
3
b)
4
c)
6
d)
2
4.
Factor out the GCF:
10x³ - 15x
a)
x(10x² - 15)
b)
5x(2x² - 3)
c)
5(2x³ - 3x)
d)
5x²(10x - 3)
5.

Factor using GCF or monomial factoring:

2n2-8n3

a)

2n2(n-4n2)

b)

2n2(1-4n)

c)

2n3(10-8n2)

d)

3n(1-4n)

6.

Factor the following polynomial by determining a GCF


21x -15y

a)

3(7x - 5y)

b)

3x(7 - 5y)

c)

7(3x - 5y)

d)

3y(7x - 5)

e)

prime

7.

Factor the following polynomial by determining a GCF


5p2 + 12q3

a)

pq( 5p + 12q2)

b)

(5 + 12)(p2 + q3)

c)

5(p2 + 12q3)

d)

12(5p2 + q3)

e)

prime

8.

Once we have a quadratic trinomial, we check to make sure it is of the form ax2 + bx + c. Our goal is to break this into its two binomial factors. To do so, we look for numbers that will multiply to ___ and add up to ____. (Use a, b, or c in your answer)

(a)  

9.

We also learned a tool to help us find those factors. Use the image to determine which numbers (in this example) multiply to 8 and add up to 6.

a)

4, 2

b)

4, 4

c)

1, 8

d)

-4, -2

10.
Factor:  x2 + 9x + 18
a)
(x + 3)(x + 6)
b)
(x - 3)(x - 6)
c)
(x + 9)(x + 2)
d)
(x + 3)2
11.
Factor:  
x2 -17x - 60
a)
(x - 20)(x + 3)
b)
(x - 3)(x + 20)
c)
(x - 3)(x - 20)
d)
(x + 3)(x + 20)
12.
x2-17x+72
a)
(x+2)(x-36)
b)
(x-8)(x+9)
c)
(x-8)(x-9)
d)
(x-4)(x-7)
13.
x2+10x+16
a)
(x+2)(x+8)
b)
(x-2)(x-8)
c)
(x+1)(x+16)
d)
(x+6)(x+10)
14.
Factor:
x2 - 30x + 225
a)
(x + 15)2
b)
(x - 15)2
c)
(x + 25)2
d)
(x - 25)2
15.
Find the product.
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
16.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
17.
Factor:
x2 - 144
a)
(x + 12)2
b)
(x - 12)(x + 12)
c)
(x - 12)2
d)
122
18.
Which is another way of correctly expressing
 (x  - 3)(x - 3)?
a)
(x2 - 32)
b)
(x2 - 3)
c)
(x + 3)(x - 3)
d)
(x - 3)2
19.

Factor the following trinomial


c2 - 12c - 45

a)

(c - 15)(c + 3)

b)

(c - 3)(c + 15)

c)

(c - 9)(c + 5)

d)

(c - 5)(c + 9)

e)

prime

20.
Factor
n2 + 16n + 63
a)
(n-7)(n+4)
b)
(n+7)(n-9)
c)
(n-3)(n-10)
d)
(n+7)(n+9)
21.
Factor
k2 - 2k - 24
a)
(k+4)(k-6)
b)
(k+4)(k+6)
c)
(k+6)(k-1)
d)
(k-4)(k+6)
22.
Factor
n2 - 13n + 40
a)
(n-5)(n-8)
b)
(n+5)(n-8)
c)
(n-5)(n+8)
d)
(n+6)(n+1)
23.
Factor:
 x² - 4x + 24
a)
prime
b)
(x + 6)(x - 4)
c)
(x - 8)(x - 3)
d)
(x - 12)(x - 2)
24.
Factor
d2 - 10d + 25
a)
(d + 5) (d - 5)
b)
(d - 15) (d + 10)
c)
(d + 5) (d - 20)
d)
(d - 5) (d - 5)
25.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
26.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
27.

Ok- enough factoring for now. Let's make sure we can still multiply, add, and subtract. Simplify the expression using the distributive property..

x3(2x2+3x)

a)

2x5+3x4

b)

2x6+3x3

c)

5x9

d)

5x

28.

-5x6(3x2 - 12x + 30)

a)

-15x8 + 60x7 - 150x6

b)

15x8 - 60x7 - 150x6

c)

8x6 - 17x + 35

d)

-8x6 + 17x - 35x2

29.
(x + 3)(x + 7)
a)
x2 + 10x + 21
b)
x2 + 21
c)
x2 + 4x + 21
d)
x2 − 10x + 21
30.
(2x − 3)(2x + 3)
a)
4x2 − 12x + 9
b)
4x2 − 9
c)
4x2 + 9
d)
4x2 + 6x − 9
31.
(3x − 6)(7x + 7)
a)
21x2 − 63x + 42
b)
21x2 − 21x − 42
c)
21x2 − 42
d)
21x2 + 63x + 42
32.
Multiply.
(b + 3)(b2 + 2b + 1)
a)
b3+6b2+6b+3
b)
b3+5b2+7b+3
c)
4b3+8b2+3b
d)
3b3+6b2+3b
33.
Multiply.
(x - 4)(x - 6)
a)
x2 -10x + 24
b)
x2 - 10x - 24
c)
x2 +10x + 24
d)
x2 + 10x - 24
34.

Multiply.

(x + 7)2

a)

x2 + 7x + 7x + 49

b)

x2 + 7x + 7

c)

7x2 + x + 7

d)

x2 + 14x + 49

35.
Add to Simplify:
 (4x - 2x3) + (5x3 - 4x + 5)
a)
3x3 + 5
b)
3x3 + 8x + 5
c)
3x2 + 5
d)
7x3 + 8x + 5
36.
Add or Subtract to Simplify:
(x5 + x3) - (6x - x3 + 6x5)
a)
-5x5 + 2x3 - 6x
b)
7x5 - 6x
c)
-5x3 + 2x2 - 6x
d)
-5x5 - 6x
37.

(3x2 + 6x - 1) + (4x2 + 5x + 9)

a)

-x2 + x - 10

b)

x2 - x + 10

c)

7x2 + 11x + 8

d)

7x2 + 11x + 10

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