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Chapter 7 Review Exercises

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Chapter 7 Review Exercises

7.1 Greatest Common Factor and Factor by Grouping

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

Exercise 1

42, 60

Answer

6

Exercise 2

450, 420

Exercise 3

90, 150, 105

Answer

15

Exercise 4

60, 294, 630

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

Exercise 5

24x42

Answer

6(4x7)

Exercise 6

35y+84

Exercise 7

15m4+6m2n

Answer

3m2(5m2+2n)

Exercise 8

24pt4+16t7

Factor by Grouping

In the following exercises, factor by grouping.

Exercise 9

axay+bxby

Answer

(a+b)(xy)

Exercise 10

x2yxy2+2x2y

Exercise 11

x2+7x3x21

Answer

(x3)(x+7)

Exercise 12

4x216x+3x12

Exercise 13

m3+m2+m+1

Answer

(m2+1)(m+1)

Exercise 14

5x5yy+x

7.2 Factor Trinomials of the form x2+bx+c

Factor Trinomials of the Form x2+bx+c

In the following exercises, factor each trinomial of the form x2+bx+c

Exercise 15

u2+17u+72

Answer

(u+8)(u+9)

Exercise 16

a2+14a+33

Exercise 17

k216k+60

Answer

(k6)(k10)

Exercise 18

r211r+28

Exercise 19

y2+6y7

Answer

(y+7)(y1)

Exercise 20

m2+3m54

Exercise 21

s22s8

Answer

(s4)(s+2)

Exercise 22

x23x10

Factor Trinomials of the Form x2+bxy+cy2

In the following examples, factor each trinomial of the form x2+bxy+cy2

Exercise 23

x2+12xy+35y2

Answer

(x+5y)(x+7y)

Exercise 24

u2+14uv+48v2

Exercise 25

a2+4ab21b2

Answer

(a+7b)(a3b)

Exercise 26

p25pq36q2

7.3 Factoring Trinomials of the form ax2+bx+c

Recognize a Preliminary Strategy to Factor Polynomials Completely

In the following exercises, identify the best method to use to factor each polynomial.

Exercise 27

y217y+42

Answer

Undo FOIL

Exercise 28

12r2+32r+5

Exercise 29

8a3+72a

Answer

Factor the GCF

Exercise 30

4mmn3n+12

Factor Trinomials of the Form ax2+bx+c with a GCF

In the following exercises, factor completely.

Exercise 31

6x2+42x+60

Answer

6(x+2)(x+5)

Exercise 32

8a2+32a+24

Exercise 33

3n412n396n2

Answer

3n2(n8)(n+4)

Exercise 34

5y4+25y270y

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

Exercise 35

2x2+9x+4

Answer

(x+4)(2x+1)

Exercise 36

3y2+17y+10

Exercise 37

18a29a+1

Answer

(3a1)(6a1)

Exercise 38

8u214u+3

Exercise 39

15p2+2p8

Answer

(5p+4)(3p2)

Exercise 40

15x2+6x2

Exercise 41

40s2s6

Answer

(5s2)(8s+3)

Exercise 42

20n27n3

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

Exercise 43

3x2+3x36

Answer

3(x+4)(x3)

Exercise 44

4x2+4x8

Exercise 45

60y285y25

Answer

5(4y+1)(3y5)

Exercise 46

18a257a21

7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

Exercise 47

25x2+30x+9

Answer

(5x+3)2

Exercise 48

16y2+72y+81

Exercise 49

36a284ab+49b2

Answer

(6a7b)2

Exercise 50

64r2176rs+121s2

Exercise 51

40x2+360x+810

Answer

10(2x+9)2

Exercise 52

75u2+180u+108

Exercise 53

2y316y2+32y

Answer

2y(y4)2

Exercise 54

5k370k2+245k

Factor Differences of Squares

In the following exercises, factor.

Exercise 55

81r225

Answer

(9r5)(9r+5)

Exercise 56

49a2144

Exercise 57

169m2n2

Answer

(13m+n)(13mn)

Exercise 58

64x2y2

Exercise 59

25p21

Answer

(5p1)(5p+1)

Exercise 60

116s2

Exercise 61

9121y2

Answer

(3+11y)(311y)

Exercise 62

100k281

Exercise 64

20x2125

Answer

5(2x5)(2x+5)

Exercise 64

18y298

Exercise 65

49u39u

Answer

u(7u+3)(7u3)

Exercise 66

169n3n

Factor Sums and Differences of Cubes

In the following exercises, factor.

Exercise 67

a3125

Answer

(a5)(a2+5a+25)

Exercise 68

b3216

Exercise 69

2m3+54

Answer

2(m+3)(m23m+9)

Exercise 70

81x3+3

7.5 General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

Exercise 71

24x3+44x2

Answer

4x2(6x+11)

Exercise 72

24a49a3

Exercise 73

16n256mn+49m2

Answer

(4n7m)2

Exercise 74

6a225a9

Exercise 75

5r2+22r48

Answer

(r+6)(5r−8)

Exercise 76

5u445u2

Exercise 77

n481

Answer

(n2+9)(n+3)(n3)

Exercise 78

64j2+225

Exercise 79

5x2+5x60

Answer

5(x3)(x+4)

Exercise 80

b364

Exercise 81

m3+125

Answer

(m+5)(m25m+25)

Exercise 82

2b22bc+5cb5c2

7.6 Quadratic Equations

Use the Zero Product Property

In the following exercises, solve.

Exercise 83

(a3)(a+7)=0

Answer

a=3, a=7

Exercise 84

(b3)(b+10)=0

Exercise 85

3m(2m5)(m+6)=0

Answer

m=0, m=6, m=52

Exercise 86

7n(3n+8)(n5)=0

Solve Quadratic Equations by Factoring

In the following exercises, solve.

Exercise 87

x2+9x+20=0

Answer

x=4, x=5

Exercise 88

y2y72=0

Exercise 89

2p211p=40

Answer

p=52, p=8

Exercise 90

q3+3q2+2q=0

Exercise 91

144m225=0

Answer

m=512, m=512

Exercise 92

4n2=36

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

Exercise 93

The product of two consecutive numbers is 462.

Answer

−21,−22

21, 22

Exercise 94

The area of a rectangular shaped patio 400 square feet. The length of the patio is 99 feet more than its width. Find the length and width.

Practice Test

In the following exercises, find the Greatest Common Factor in each expression.

Exercise 95

14y42

Answer

7(y6)

Exercise 96

6x230x

Exercise 97

80a2+120a3

Answer

40a2(2+3a)

Exercise 98

5m(m1)+3(m1)

In the following exercises, factor completely.

Exercise 99

x2+13x+36

Answer

(x+7)(x+6)

Exercise 100

p2+pq12q2

Exercise 101

3a36a272a

Answer

3a(a+4)(a6)

Exercise 102

s225s+84

Exercise 103

5n2+30n+45

Answer

5(n+3)2

Exercise 104

64y249

Exercise 105

xy8y+7x56

Answer

(x8)(y+7)

Exercise 106

40r2+810

Exercise 107

9s212s+4

Answer

(3s2)2

Exercise 1008

n2+12n+36

Exercise 109

100a2

Answer

(10a)(10+a)

Exercise 110

6x211x10

Exercise 111

3x275y2

Answer

3(x+5y)(x5y)

Exercise 112

c31000d3

Exercise 113

ab3b2a+6

Answer

(a3)(b2)

Exercise 114

6u2+3u18

Exercise 115

8m2+22m+5

Answer

(4m+1)(2m+5)

In the following exercises, solve.

Exercise 116

x2+9x+20=0

Exercise 117

y2=y+132

Answer

y=11, y=12

Exercise 118

5a2+26a=24

Exercise 119

9b29=0

Answer

b=1, b=1

Exercise 120

16m2=0

Exercise 121

4n2+19n+21=0

Answer

n=74, n=−3

Exercise 122

(x3)(x+2)=6

Exercise 123

The product of two consecutive integers is 156.

Answer

12 and 13; −13 and −12

Exercise 124

The area of a rectangular place mat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.


This page titled Chapter 7 Review 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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