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Mathematics LibreTexts

7.1E: Exercises

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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

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

x

Exercise 8

21b2, 14b

Exercise 9

8w2, 24w3

Answer

8w2

Exercise 10

30x2, 18x3

Exercise 11

10p3q, 12pq2

Answer

2pq

Exercise 12

8a2b3, 10ab2

Exercise 13

12m2n3, 30m5n3

Answer

6m2n3

Exercise 14

28x2y4, 42x4y4

Exercise 15

10a3, 12a2, 14a

Answer

2a

Exercise 16

20y3, 28y2, 40y

Exercise 17

35x3, 10x4, 5x5

Answer

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

3(2m+3)

Exercise 22

14p+35

Exercise 23

9q+9

Answer

9(q+1)

Exercise 24

7r+7

Exercise 25

8m8

Answer

8(m1)

Exercise 26

4n4

Exercise 27

9n63

Answer

9(n7)

Exercise 28

45b18

Exercise 29

3x2+6x9

Answer

3(x2+2x3)

Exercise 30

4y2+8y4

Exercise 31

8p2+4p+2

Answer

2(4p2+2p+1)

Exercise 32

10q2+14q+20

Exercise 33

8y3+16y2

Answer

8y2(y+2)

Exercise 34

12x310x

Exercise 35

5x315x2+20x

Answer

5x(x23x+4)

Exercise 36

8m240m+16

Exercise 37

12xy2+18x2y230y3

Answer

6y2(2x+3x25y)

Exercise 38

21pq2+35p2q228q3

Exercise 39

2x4

Answer

2(x+2)

Exercise 40

3b+12

Exercise 41

5x(x+1)+3(x+1)

Answer

(x+1)(5x+3)

Exercise 42

2x(x1)+9(x1)

Exercise 43

3b(b2)13(b2)

Answer

(b2)(3b13)

Exercise 44

6m(m5)7(m5)

​​​​​​Factor by Grouping

In the following exercises, factor by grouping.

Exercise 45

xy+2y+3x+6

Answer

(y+3)(x+2)

Exercise 46

mn+4n+6m+24

Exercise 47

uv9u+2v18

Answer

(u+2)(v9)

Exercise 48

pq10p+8q80

Exercise 49

b2+5b4b20

Answer

(b4)(b+5)

Exercise 50

m2+6m12m72

Exercise 51

p2+4p9p36

Answer

(p9)(p+4)

Exercise 52

x2+5x3x15

Mixed Practice

In the following exercises, factor.

Exercise 53

20x10

Answer

10(2x+1)

Exercise 54

5x3x2+x

Exercise 55

3x37x2+6x14

Answer

(x2+2)(3x7)

Exercise 56

x3+x2x1

Exercise 57

x2+xy+5x+5y

Answer

(x+y)(x+5)

Exercise 58

5x33x25x3

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 w26w, where w= width. Factor the greatest common factor from the polynomial.

Answer

w(w6)

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.

This table has the following statements all to be preceded by “I can…”. The first is “find the greatest common factor of two or more expressions”. The second is “factor the greatest common factor from a polynomial”. The third is “factor by grouping”. In the columns beside these statements are the headers, “confidently”, “with some help”, and “no-I don’t get it!”.

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.


This page titled 7.1E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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