7.1E: Exercises
- Page ID
- 30437
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Practice Makes Perfect
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
Exercise 1
8,18
- Answer
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2
Exercise 2
24,40
Exercise 3
72,162
- Answer
-
18
Exercise 4
150,275
Exercise 5
10a,50
- Answer
-
10
Exercise 6
5b,30
Exercise 7
3x, 10x2
- Answer
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x
Exercise 8
21b2, 14b
Exercise 9
8w2, 24w3
- Answer
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8w2
Exercise 10
30x2, 18x3
Exercise 11
10p3q, 12pq2
- Answer
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2pq
Exercise 12
8a2b3, 10ab2
Exercise 13
12m2n3, 30m5n3
- Answer
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6m2n3
Exercise 14
28x2y4, 42x4y4
Exercise 15
10a3, 12a2, 14a
- Answer
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2a
Exercise 16
20y3, 28y2, 40y
Exercise 17
35x3, 10x4, 5x5
- Answer
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5x3
Exercise 18
27p2, 45p3, 9p4
Factor the Greatest Common Factor from a Polynomial
In the following exercises, factor the greatest common factor from each polynomial.
Exercise 19
4x+20
- Answer
-
4(x+5)
Exercise 20
8y+16
Exercise 21
6m+9
- Answer
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3(2m+3)
Exercise 22
14p+35
Exercise 23
9q+9
- Answer
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9(q+1)
Exercise 24
7r+7
Exercise 25
8m−8
- Answer
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8(m−1)
Exercise 26
4n−4
Exercise 27
9n−63
- Answer
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9(n−7)
Exercise 28
45b−18
Exercise 29
3x2+6x−9
- Answer
-
3(x2+2x−3)
Exercise 30
4y2+8y−4
Exercise 31
8p2+4p+2
- Answer
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2(4p2+2p+1)
Exercise 32
10q2+14q+20
Exercise 33
8y3+16y2
- Answer
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8y2(y+2)
Exercise 34
12x3−10x
Exercise 35
5x3−15x2+20x
- Answer
-
5x(x2−3x+4)
Exercise 36
8m2−40m+16
Exercise 37
12xy2+18x2y2−30y3
- Answer
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6y2(2x+3x2−5y)
Exercise 38
21pq2+35p2q2−28q3
Exercise 39
−2x−4
- Answer
-
−2(x+2)
Exercise 40
−3b+12
Exercise 41
5x(x+1)+3(x+1)
- Answer
-
(x+1)(5x+3)
Exercise 42
2x(x−1)+9(x−1)
Exercise 43
3b(b−2)−13(b−2)
- Answer
-
(b−2)(3b−13)
Exercise 44
6m(m−5)−7(m−5)
In the following exercises, factor by grouping.
Exercise 45
xy+2y+3x+6
- Answer
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(y+3)(x+2)
Exercise 46
mn+4n+6m+24
Exercise 47
uv−9u+2v−18
- Answer
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(u+2)(v−9)
Exercise 48
pq−10p+8q−80
Exercise 49
b2+5b−4b−20
- Answer
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(b−4)(b+5)
Exercise 50
m2+6m−12m−72
Exercise 51
p2+4p−9p−36
- Answer
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(p−9)(p+4)
Exercise 52
x2+5x−3x−15
In the following exercises, factor.
Exercise 53
−20x−10
- Answer
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−10(2x+1)
Exercise 54
5x3−x2+x
Exercise 55
3x3−7x2+6x−14
- Answer
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(x2+2)(3x−7)
Exercise 56
x3+x2−x−1
Exercise 57
x2+xy+5x+5y
- Answer
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(x+y)(x+5)
Exercise 58
5x3−3x2−5x−3
Everyday Math
Exercise 59
Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression w2−6w, where w= width. Factor the greatest common factor from the polynomial.
- Answer
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w(w−6)
Exercise 60
Height of a baseball The height of a baseball t seconds after it is hit is given by the expression −16t2+80t+4
Writing Exercises
Exercise 61
The greatest common factor of 36 and 60 is 12. Explain what this means.
- Answer
-
Answers will vary.
Exercise 62
What is the GCF of y4, y5, and y10? Write a general rule that tells you how to find the GCF of ya, yb, and yc.
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. If most of your checks were:
…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!
…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential—every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.