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M2 Unit 2 Factoring

Total questions: 40

Worksheet time: 4hrs 13mins

Name
Class
Date
1.
Factor completely:
16x2 - 20xy
a)
4 (4x2 - 5xy)
b)
4x (4x - 5y)
c)
4x2 (4 - 5y)
d)
2(duck)
2.
Factor completely:
4x2y - 12xy + 5y
a)
(2xy - 1) (2x - 5)
b)
prime
c)
y (2x - 1) (2x - 5)
d)
4 (xy - 5) (x - 1)
3.
Factor completely:
y2 - 7y + 12
a)
(y - 3) (y - 4)
b)
(y + 3) (y - 4)
c)
(y + 3) (y + 4)
d)
(y - 2) (y - 6)
4.
Factor completely:
2x2 + 7x + 6
a)
(2x - 3) (x - 2)
b)
(2x + 3) (x + 2)
c)
(x + 3) (2x + 2)
d)
prime
5.
Factor completely:
4x2 - 121
a)
(2x + 11) (11 - 2x)
b)
(2x - 11) (2x - 11)
c)
(2x + 11) (2x + 11)
d)
(2x + 11) (2x - 11)
6.
Factor completely:
x2 - 5x + 3
a)
(x + 3) (x + 1)
b)
(x - 3) (x - 1)
c)
prime
d)
(x - 3) (x + 1)
7.
Factor completely:
-8x2 + 10x + 3
a)
(2x - 3) (-4x - 1)
b)
-1 (2x - 3) (4x + 1)
c)
-1 (-2x + 3) (4x + 1)
d)
(-2x + 3) (4x + 1)
8.
Factor completely:
49p2 + 84p + 36
a)
(7p - 6)(7p - 6)
b)
(7p - 6)2
c)
(7p + 6)(7p - 6)
d)
(7p + 6)(7p + 6)
9.
8r3 + 16r2
a)
4r2(2r + 4)
b)
8r2(r + 2)
c)
8(r3 + r2)
d)
4(r3 + 2r2)
10.
What is the GCF? 5x2+20x
a)
5
b)
x
c)
5x
d)
20x
11.
−28a6 +20a4 −40a3
Find the GCF
(greatest common factor) 
a)
4a2
b)
4a3
12.
2x3y8 + 6x4y2 + 10x5y10 what is the GCF? 
a)
2x3y2
b)
x3y2
c)
2
d)
-x3y2
13.
Factor 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)
14.

What is the first step in factoring this problem?

x2 + x - 6

a)

Multiply

b)

List the factors of -6

c)

Add the factors of -6

d)

Factor out the GCF

15.

Find the factors of

x2 + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

16.

What is the first step in factoring this problem?

x2 - 5x - 36

a)

Multiply

b)

List the factors of -36

c)

Add the factors of -36

d)

Factor out the GCF

17.

Find the factors of

x2 - 5x - 36

a)

(x + 4)(x - 9)

b)

(x - 4)(x + 9)

c)

(x - 9)(x + 6)

d)

(x + 4)(x + 9)

18.

Find the factors of

2b2 + 14b - 16

a)

2(b - 1)(b + 8)

b)

6(b - 1)(b - 5)

c)

2(b + 1)(b - 8)

d)

2(b - 1)(b - 8)

19.

Find the factors of

5k2 - 18k + 9

a)

(5k - 3)(k - 3)

b)

(3k + 5)(k - 10)

c)

(2k - 1)(k + 6)

d)

(5k + 7)(k + 6)

20.

Find the factors of

3b2 + 17b + 20

a)

(2b - 5)(b - 7)

b)

(5b - 7)(b - 2)

c)

(b + 5)(3b + 4)

d)

(3b + 5)(b + 4)

21.
Factor completely:
x³+7x²-2x-14
a)
(x²-2)(x-7)
b)
(x²+2)(x-7)
c)
(x²+2)(x+7)
d)
(x²-2)(x+7)
22.
Factor completely:
2x3 + 5x2 - 8x - 20
a)
(x2 - 4)(2x + 5)
b)
(2x - 5)(x2 + 4)
c)
(2x2 - 4)(x + 5)
d)
(x - 2)(x + 2)(2x + 5)
23.
Factor: 8x3 - 1
a)
(2x - 1)(4x2 + 2x + 1)
b)
(2x + 1)(4x2 - 2x + 1)
c)
(2x - 1)(4x2 - 2x - 1)
d)
(2x + 1)(4x2 +2x + 1)
24.

Factor Completely

5x2-28x+32

a)

(3x-10)(x+6)

b)

(x-8)(5x-4)

c)

(5x-8)(x-4)

d)

(5x-8)(x+7)

25.

Factor Completely:

k4 - 10k2 - 39

a)

(k2 - 13)(k2 + 3)

b)

(k - 13)(k + 3)

c)

(k2 + 15)(k2 - 3)

d)

(k + 13)(k - 3)

26.
Combine like terms to simplify:
 (5x + 2) + (4x + 5)
a)
9x -7
b)
-9x-11
c)
9x+7
d)
x+7
27.
Simplify each expression.
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3 
b)
-7n2 - 8n + 3 
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
28.
Find the sum.
(3y2 + y3 - 5) + (4y2 -4y + 2y3 + 8)
a)
3y3 + 7y2 - 4y + 3
b)
4y2 + 3y3 - y + 3
c)
-y4 + 2y3 -y - 4
d)
4y3 + 3y2 -3y + 1
29.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
30.
Simplify each expression.
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
31.
Add or Subtract to Simplify:
(4n4 - 8n + 4) - (8n2 + 4n4 + 1)
a)
-8n2 - 8n + 3 
b)
-7n2 - 8n + 3 
c)
-6n2 - 8n + 3
d)
-7n2 - 4n + 3
32.
Simplify:
2x (-2x - 3)
a)
-4x - 3
b)
x2 - 3
c)
-4x2 - 6x
d)
-4x - 6
33.
Multiply.
(x + 2)(x + 3)
a)
x2 + 5x + 6
b)
x2 + x + 6
c)
x2 + 5x + 5
d)
x2 + 6x + 6
34.
Multiply.
(x - 5)(x + 1)
a)
x2 - 4x - 5
b)
x2 + 6x - 5
c)
x2 - 5x - 4
d)
x2 - 4x - 4
35.
Multiply.
(x + 7)(x - 2)
a)
x2 - 5x + 5
b)
x2 - 9x - 14
c)
x2 - 5x - 14
d)
x2 + 5x - 14
36.
Multiply.
-3x2(7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
37.
Multiply.
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
38.
Multiply.
(3x - 5)(4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
39.
Multiply.
(5x + 2)(x2 - 3x + 6)
a)
5x3 - 17x2 +24x +12
b)
5x3 + 17x2 - 24x +12
c)
5x3 - 13x2 + 24x +12
d)
5x3 +13x2 - 24x - 12
40.
Multiply.
(b + 3)(b2 + 2b + 1)
a)
b3+6b2+6b+3
b)
b3+5b2+7b+3
c)
4b3+8b2+3b
d)
3b3+6b2+3b

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