Chapter 6 Review Exercises
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Chapter 6 Review Exercises
Add and Subtract Polynomials
Identify Polynomials, Monomials, Binomials and Trinomials
In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.
Exercise 1
- 11c4−23c2+1
- 9p3+6p2−p−5
- 37x+514
- 10
- 2y−12
Exercise 2
- a2−b2
- 24d3
- x2+8x−10
- m2n2−2mn+6
- 7y3+y2−2y−4
- Answer
-
- binomial
- monomial
- trinomial
- trinomial
- other polynomial
Determine the Degree of Polynomials
In the following exercises, determine the degree of each polynomial.
Exercise 3
- 3x2+9x+10
- 14a2bc
- 6y+1
- n3−4n2+2n−8
- −19
Exercise 4
- 5p3−8p2+10p−4
- −20q4
- x2+6x+12
- 23r2s2−4rs+5
- 100
- Answer
-
- 3
- 4
- 2
- 4
- 0
Add and Subtract Monomials
In the following exercises, add or subtract the monomials.
Exercise 5
5y3+8y3
Exercise 6
−14k+19k
- Answer
-
5k
Exercise 7
12q−(−6q)
Exercise 8
−9c−18c
- Answer
-
−27c
Exercise 9
12x−4y−9x
Exercise 2
3m2+7n2−3m2
- Answer
-
7n2
Exercise 3
6x2y−4x+8xy2
Exercise 4
13a+b
- Answer
-
13a+b
Add and Subtract Polynomials
In the following exercises, add or subtract the polynomials.
Exercise 5
(5x2+12x+1)+(6x2−8x+3)
Exercise 6
(9p2−5p+3)+(4p2−4)
- Answer
-
13p2−5p−1
Exercise 7
(10m2−8m−1)−(5m2+m−2)
Exercise 8
(7y2−8y)−(y−4)
- Answer
-
7y2−9y+4
Exercise 9
Subtract
(3s2+10) from (15s2−2s+8)
Exercise 10
Find the sum of (a2+6a+9) and (5a3−7)
- Answer
-
5a3+a2+6a+2
Evaluate a Polynomial for a Given Value of the Variable
In the following exercises, evaluate each polynomial for the given value.
Exercise 11
Evaluate 3y2−y+1 when:
- y=5
- y=−1
- y=0
Exercise 12
Evaluate 10−12x when:
- x=3
- x=0
- x=−1
- Answer
-
- −26
- 10
- 22
Exercise 13
Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial −16t2+200 gives the height of a stone t seconds after it is dropped from the cliff. Find the height after t=3 seconds.
Exercise 14
A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial −4p2+460p. Find the revenue received when p=75 dollars.
- Answer
-
12,000
Use Multiplication Properties of Exponents
Simplify Expressions with Exponents
In the following exercises, simplify.
Exercise 15
104
Exercise 16
171
- Answer
-
17
Exercise 17
(29)2
Exercise 18
(0.5)3
- Answer
-
0.125
Exercise 19
(−2)6
Exercise 20
−26
- Answer
-
−64
Simplify Expressions Using the Product Property for Exponents
In the following exercises, simplify each expression.
Exercise 21
x4⋅x3
Exercise 22
p15⋅p16
- Answer
-
p31
Exercise 23
410⋅46
Exercise 24
8⋅85
- Answer
-
86
Exercise 25
n⋅n2⋅n4
Exercise 26
yc⋅y3
- Answer
-
yc+3
Simplify Expressions Using the Power Property for Exponents
In the following exercises, simplify each expression.
Exercise 27
(m3)5
Exercise 28
(53)2
- Answer
-
56
Exercise 29
(y4)x
Exercise 30
(3r)s
- Answer
-
3rs
Simplify Expressions Using the Product to a Power Property
In the following exercises, simplify each expression.
Exercise 31
(4a)2
Exercise 32
(−5y)3
- Answer
-
−125y3
Exercise 33
(2mn)5
Exercise 34
(10xyz)3
- Answer
-
1000x3y3z3
Simplify Expressions by Applying Several Properties
In the following exercises, simplify each expression.
Exercise 35
(p2)5⋅(p3)6
Exercise 36
(4a3b2)3
- Answer
-
64a9b6
Exercise 37
(5x)2(7x)
Exercise 38
(2q3)4(3q)2
- Answer
-
48q14
Exercise 39
(13x2)2(12x)3
Exercise 40
(25m2n)3
- Answer
-
8125m6n3
Multiply Monomials
In the following exercises 8, multiply the monomials.
Exercise 41
(−15x2)(6x4)
Exercise 42
(−9n7)(−16n)
- Answer
-
144n8
Exercise 43
(7p5q3)(8pq9)
Exercise 44
(59ab2)(27ab3)
- Answer
-
15a2b5
Multiply Polynomials
Multiply a Polynomial by a Monomial
In the following exercises, multiply.
Exercise 45
7(a+9)
Exercise 46
−4(y+13)
- Answer
-
−4y−52
Exercise 47
−5(r−2)
Exercise 48
p(p+3)
- Answer
-
p2+3p
Exercise 49
−m(m+15)
Exercise 50
−6u(2u+7)
- Answer
-
−12u2−42u
Exercise 51
9(b2+6b+8)
Exercise 52
3q2(q2−7q+6)3
- Answer
-
3q4−21q3+18q2
Exercise 53
(5z−1)z
Exercise 54
(b−4)⋅11
- Answer
-
11b−44
Multiply a Binomial by a Binomial
In the following exercises, multiply the binomials using:
- the Distributive Property,
- the FOIL method,
- the Vertical Method.
Exercise 55
(x−4)(x+10)
Exercise 56
(6y−7)(2y−5)
- Answer
-
- 12y2−44y+35
- 12y2−44y+35
- 12y2−44y+35
In the following exercises, multiply the binomials. Use any method.
Exercise 57
(x+3)(x+9)
Exercise 58
(y−4)(y−8)
- Answer
-
y2−12y+32
Exercise 59
(p−7)(p+4)
Exercise 60
(q+16)(q−3)
- Answer
-
q2+13q−48
Exercise 61
(5m−8)(12m+1)
Exercise 62
(u2+6)(u2−5)
- Answer
-
u4+u2−30
Exercise 63
(9x−y)(6x−5)
Exercise 64
(8mn+3)(2mn−1)
- Answer
-
16m2n2−2mn−3
Multiply a Trinomial by a Binomial
In the following exercises, multiply using
- the Distributive Property,
- the Vertical Method.
Exercise 65
(n+1)(n2+5n−2)
Exercise 66
(3x−4)(6x2+x−10)
- Answer
-
- 18x3−21x2−34x+40
- 18x3−21x2−34x+40
In the following exercises, multiply. Use either method.
Exercise 67
(y−2)(y2−8y+9)
Exercise 68
(7m+1)(m2−10m−3)
- Answer
-
7m3−69m2−31m−3
Special Products
Square a Binomial Using the Binomial Squares Pattern
In the following exercises, square each binomial using the Binomial Squares Pattern.
Exercise 69
(c+11)2
Exercise 70
(q−15)2
- Answer
-
q2−30q+225
Exercise 71
(x+13)2
Exercise 72
(8u+1)2
- Answer
-
64u2+16u+1
Exercise 73
(3n3−2)2
Exercise 74
(4a−3b)2
- Answer
-
16a2−24ab+9b2
Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern.
Exercise 75
(s−7)(s+7)
Exercise 76
(y+25)(y−25)
- Answer
-
y2−425
Exercise 77
(12c+13)(12c−13)
Exercise 78
(6−r)(6+r)
- Answer
-
36−r2
Exercise 79
(u+34v)(u−34v)
Exercise 80
(5p4−4q3)(5p4+4q3)
- Answer
-
25p8−16q6
Recognize and Use the Appropriate Special Product Pattern
In the following exercises, find each product.
Exercise 81
(3m+10)2
Exercise 82
(6a+11)(6a−11)
- Answer
-
36a2−121
Exercise 83
(5x+y)(x−5y)
Exercise 84
(c4+9d)2
- Answer
-
c8+18c4d+81d2
Exercise 85
(p5+q5)(p5−q5)
Exercise 86
(a2+4b)(4a−b2)
- Answer
-
4a3+3a2b−4b3
Divide Monomials
Simplify Expressions Using the Quotient Property for Exponents
In the following exercises, simplify.
Exercise 87
u24u6
Exercise 88
1025105
- Answer
-
1020
Exercise 89
3436
Exercise 90
v12v48
- Answer
-
1v36
Exercise 91
xx5
Exercise 92
558
- Answer
-
157
Simplify Expressions with Zero Exponents
In the following exercises, simplify.
Exercise 93
750
Exercise 94
x0
- Answer
-
1
Exercise 95
−120
Exercise 96
(−120)(−12)0
- Answer
-
1
Exercise 97
25x0
Exercise 98
(25x)0
- Answer
-
1
Exercise 99
19n0−25m0
Exercise 100
(19n)0−(25m)0
- Answer
-
0
Simplify Expressions Using the Quotient to a Power Property
In the following exercises, simplify.
Exercise 101
(25)3
Exercise 102
(m3)4
- Answer
-
m481
Exercise 103
(rs)8
Exercise 104
(x2y)6
- Answer
-
x664y6
Simplify Expressions by Applying Several Properties
In the following exercises, simplify.
Exercise 105
(x3)5x9
Exercise 106
n10(n5)2
- Answer
-
1
Exercise 107
(q6q8)3
Exercise 108
(r8r3)4
- Answer
-
r20
Exercise 109
(c2d5)9
Exercise 110
(3x42y2)5
- Answer
-
343x2032y10
Exercise 111
(v3v9v6)4
Exercise 112
(3n2)4(−5n4)3(−2n5)2
- Answer
-
−10,125n104
Divide Monomials
In the following exercises, divide the monomials.
Exercise 113
−65y14÷5y2
Exercise 114
64a5b9−16a10b3
- Answer
-
−4b6a5
Exercise 115
144x15y8z318x10y2z12
Exercise 116
(8p6q2)(9p3q5)16p8q7
- Answer
-
9p2
Divide Polynomials
Divide a Polynomial by a Monomial
In the following exercises, divide each polynomial by the monomial.
Exercise 117
42z2−18z6
Exercise 118
(35x2−75x)÷5x
- Answer
-
7x−15
Exercise 119
81n4+105n2−3
Exercise 120
550p6−300p410p3
- Answer
-
55p3−30p
Exercise 121
(63xy3+56x2y4)÷(7xy)
Exercise 122
96a5b2−48a4b3−56a2b48ab2
- Answer
-
12a4−6a3b−7ab2
Exercise 123
57m2−12m+1−3m
Exercise 124
105y5+50y3−5y5y3
- Answer
-
21y2+10−1y2
Divide a Polynomial by a Binomial
In the following exercises, divide each polynomial by the binomial.
Exercise 125
(k2−2k−99)÷(k+9)
Exercise 126
(v2−16v+64)÷(v−8)
- Answer
-
v−8
Exercise 127
(3x2−8x−35)÷(x−5)
Exercise 128
(n2−3n−14)÷(n+3)
- Answer
-
n−6+4n+3
Exercise 129
(4m3+m−5)÷(m−1)
Exercise 130
(u3−8)÷(u−2)
- Answer
-
u2+2u+4
Integer Exponents and Scientific Notation
Use the Definition of a Negative Exponent
In the following exercises, simplify.
Exercise 131
9−2
Exercise 132
(−5)−3
- Answer
-
−1125
Exercise 133
3⋅4−3
Exercise 134
(6u)−3
- Answer
-
1216u3
Exercise 135
(25)−1
Exercise 136
(34)−2
- Answer
-
169
Simplify Expressions with Integer Exponents
In the following exercises, simplify.
Exercise 137
p−2⋅p8
Exercise 138
q−6⋅q−5
- Answer
-
1q11
Exercise 139
(c−2d)(c−3d−2)
Exercise 140
(y8)−1
- Answer
-
1y8
Exercise 141
(q−4)−3
Exercise 142
a8a12
- Answer
-
1a4
Exercise 143
n5n−4
Exercise 144
r−2r−3
- Answer
-
r
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
Exercise 145
8,500,000
Exercise 146
0.00429
- Answer
-
4.29×10−3
Exercise 147
The thickness of a dime is about 0.053 inches.
Exercise 148
In 2015, the population of the world was about 7,200,000,000 people.
- Answer
-
7.2×109
Convert Scientific Notation to Decimal Form
In the following exercises, convert each number to decimal form.
Exercise 149
3.8×105
Exercise 150
1.5×1010
- Answer
-
15,000,000,000
Exercise 151
9.1×10−7
Exercise 152
5.5×10−1
- Answer
-
0.55
Multiply and Divide Using Scientific Notation
In the following exercises, multiply and write your answer in decimal form.
Exercise 153
(2×105)(4×10−3)
Exercise 154
(3.5×10−2)(6.2×10−1)
- Answer
-
0.0217
In the following exercises, divide and write your answer in decimal form.
Exercise 155
8×1054×10−1
Exercise 156
9×10−53×102
- Answer
-
0.0000003
Chapter Practice Test
Exercise 1
For the polynomial 10x4+9y2−1
ⓐ Is it a monomial, binomial, or trinomial?
ⓑ What is its degree?
In the following exercises, simplify each expression.
Exercise 2
(12a2−7a+4)+(3a2+8a−10)
- Answer
-
15a2+a−6
Exercise 3
(9p2−5p+1)−(2p2−6)
Exercise 4
(−25)3
- Answer
-
−8125
Exercise 5
u⋅u4
Exercise 6
(4a3b5)2
- Answer
-
16a6b10
Exercise 7
(−9r4s5)(4rs7)
Exercise 8
3k(k2−7k+13)
- Answer
-
3k3−21k2+39k
Exercise 9
(m+6)(m+12)
Exercise 10
(v−9)(9v−5)
- Answer
-
9v2−86v+45
Exercise 11
(4c−11)(3c−8)
Exercise 12
(n−6)(n2−5n+4)
- Answer
-
n3−11n2+34n−24
Exercise 13
(2x−15y)(5x+7y)
Exercise 14
(7p−5)(7p+5)
- Answer
-
49p2−25
Exercise 15
(9v−2)2
Exercise 16
38310
- Answer
-
19
Exercise 17
(m4⋅mm3)6
Exercise 18
(87x15y3z22)0
- Answer
-
1
Exercise 19
80c8d216cd10
Exercise 20
12x2+42x−62x
- Answer
-
6x+21−3x
Exercise 21
(70xy4+95x3y)÷5xy
Exercise 22
64x3−14x−1
- Answer
-
16x2+4x+1
Exercise 23
(y2−5y−18)÷(y+3)
Exercise 24
5−2
- Answer
-
125
Exercise 25
(4m)−3
Exercise 26
q−4⋅q−5
- Answer
-
1q9
Exercise 27
n−2n−10
Exercise 28
Convert 83,000,000 to scientific notation.
- Answer
-
8.3×107
Exercise 29
Convert 6.91×10−5 to decimal form.
In the following exercises, simplify, and write your answer in decimal form.
Exercise 30
(3.4×109)(2.2×10−5)
- Answer
-
74,800
Exercise 31
8.4×10−34×103
Exercise 32
A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial −16t2+1000 gives the height of the package t seconds a after it was dropped. Find the height when t=6 seconds.
- Answer
-
424 feet