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.
42, 60
- Answer
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6
450, 420
90, 150, 105
- Answer
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15
60, 294, 630
Factor the Greatest Common Factor from a Polynomial
In the following exercises, factor the greatest common factor from each polynomial.
24x−42
- Answer
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6(4x−7)
35y+84
15m4+6m2n
- Answer
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3m2(5m2+2n)
24pt4+16t7
Factor by Grouping
In the following exercises, factor by grouping.
ax−ay+bx−by
- Answer
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(a+b)(x−y)
x2y−xy2+2x−2y
x2+7x−3x−21
- Answer
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(x−3)(x+7)
4x2−16x+3x−12
m3+m2+m+1
- Answer
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(m2+1)(m+1)
5x−5y−y+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
u2+17u+72
- Answer
-
(u+8)(u+9)
a2+14a+33
k2−16k+60
- Answer
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(k−6)(k−10)
r2−11r+28
y2+6y−7
- Answer
-
(y+7)(y−1)
m2+3m−54
s2−2s−8
- Answer
-
(s−4)(s+2)
x2−3x−10
Factor Trinomials of the Form x2+bxy+cy2
In the following examples, factor each trinomial of the form x2+bxy+cy2
x2+12xy+35y2
- Answer
-
(x+5y)(x+7y)
u2+14uv+48v2
a2+4ab−21b2
- Answer
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(a+7b)(a−3b)
p2−5pq−36q2
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.
y2−17y+42
- Answer
-
Undo FOIL
12r2+32r+5
8a3+72a
- Answer
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Factor the GCF
4m−mn−3n+12
Factor Trinomials of the Form ax2+bx+c with a GCF
In the following exercises, factor completely.
6x2+42x+60
- Answer
-
6(x+2)(x+5)
8a2+32a+24
3n4−12n3−96n2
- Answer
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3n2(n−8)(n+4)
5y4+25y2−70y
Factor Trinomials Using the “ac” Method
In the following exercises, factor.
2x2+9x+4
- Answer
-
(x+4)(2x+1)
3y2+17y+10
18a2−9a+1
- Answer
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(3a−1)(6a−1)
8u2−14u+3
15p2+2p−8
- Answer
-
(5p+4)(3p−2)
15x2+6x−2
40s2−s−6
- Answer
-
(5s−2)(8s+3)
20n2−7n−3
Factor Trinomials with a GCF Using the “ac” Method
In the following exercises, factor.
3x2+3x−36
- Answer
-
3(x+4)(x−3)
4x2+4x−8
60y2−85y−25
- Answer
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5(4y+1)(3y−5)
18a2−57a−21
7.4 Factoring Special Products
Factor Perfect Square Trinomials
In the following exercises, factor.
25x2+30x+9
- Answer
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(5x+3)2
16y2+72y+81
36a2−84ab+49b2
- Answer
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(6a−7b)2
64r2−176rs+121s2
40x2+360x+810
- Answer
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10(2x+9)2
75u2+180u+108
2y3−16y2+32y
- Answer
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2y(y−4)2
5k3−70k2+245k
In the following exercises, factor.
81r2−25
- Answer
-
(9r−5)(9r+5)
49a2−144
169m2−n2
- Answer
-
(13m+n)(13m−n)
64x2−y2
25p2−1
- Answer
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(5p−1)(5p+1)
1−16s2
9−121y2
- Answer
-
(3+11y)(3−11y)
100k2−81
20x2−125
- Answer
-
5(2x−5)(2x+5)
18y2−98
49u3−9u
- Answer
-
u(7u+3)(7u−3)
169n3−n
Factor Sums and Differences of Cubes
In the following exercises, factor.
a3−125
- Answer
-
(a−5)(a2+5a+25)
b3−216
2m3+54
- Answer
-
2(m+3)(m2−3m+9)
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.
24x3+44x2
- Answer
-
4x2(6x+11)
24a4−9a3
16n2−56mn+49m2
- Answer
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(4n−7m)2
6a2−25a−9
5r2+22r−48
- Answer
-
(r+6)(5r−8)
5u4−45u2
n4−81
- Answer
-
(n2+9)(n+3)(n−3)
64j2+225
5x2+5x−60
- Answer
-
5(x−3)(x+4)
b3−64
m3+125
- Answer
-
(m+5)(m2−5m+25)
2b2−2bc+5cb−5c2
7.6 Quadratic Equations
Use the Zero Product Property
In the following exercises, solve.
(a−3)(a+7)=0
- Answer
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a=3, a=−7
(b−3)(b+10)=0
3m(2m−5)(m+6)=0
- Answer
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m=0, m=−6, m=52
7n(3n+8)(n−5)=0
Solve Quadratic Equations by Factoring
In the following exercises, solve.
x2+9x+20=0
- Answer
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x=−4, x=−5
y2−y−72=0
2p2−11p=40
- Answer
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p=−52, p=8
q3+3q2+2q=0
144m2−25=0
- Answer
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m=512, m=−512
4n2=36
Solve Applications Modeled by Quadratic Equations
In the following exercises, solve.
The product of two consecutive numbers is 462.
- Answer
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−21,−22
21, 22
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.
14y−42
- Answer
-
7(y−6)
−6x2−30x
80a2+120a3
- Answer
-
40a2(2+3a)
5m(m−1)+3(m−1)
In the following exercises, factor completely.
x2+13x+36
- Answer
-
(x+7)(x+6)
p2+pq−12q2
3a3−6a2−72a
- Answer
-
3a(a+4)(a−6)
s2−25s+84
5n2+30n+45
- Answer
-
5(n+3)2
64y2−49
xy−8y+7x−56
- Answer
-
(x−8)(y+7)
40r2+810
9s2−12s+4
- Answer
-
(3s−2)2
n2+12n+36
100−a2
- Answer
-
(10−a)(10+a)
6x2−11x−10
3x2−75y2
- Answer
-
3(x+5y)(x−5y)
c3−1000d3
ab−3b−2a+6
- Answer
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(a−3)(b−2)
6u2+3u−18
8m2+22m+5
- Answer
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(4m+1)(2m+5)
In the following exercises, solve.
x2+9x+20=0
y2=y+132
- Answer
-
y=−11, y=12
5a2+26a=24
9b2−9=0
- Answer
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b=1, b=−1
16−m2=0
4n2+19n+21=0
- Answer
-
n=−74, n=−3
(x−3)(x+2)=6
The product of two consecutive integers is 156.
- Answer
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12 and 13; −13 and −12
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.