Test Bank for College Algebra Enhanced with Graphing Utilities , 7th Edition

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TEST I TEM F ILE
(DOWNLOAD O NLY)
COLLEGE ALGEBRA
Enhanced with Graphing Utilities
SEVENTH EDITION
M ICHAEL SULLIVAN
Chicago State University

Ch. 0 Chapter R: Review
0.1 Real Numbers
1 Work with Sets
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set.
1) B ∪ C
A) {1, 2, 3, 4, 5, 7, 9} B) { } C) {0} D) {1, 2, 3, 5, 7, 9}
2) A ∪ C
A) {1, 2, 3, 4, 5, 8, 9} B) {4, 6, 7, 9} C) {1} D) {1, 2, 3, 5, 7, 9}
3) A ∩ B
A) {2, 3, 5} B) {1, 2, 3, 5, 7, 8} C) {2, 3, 5, 7} D) {1, 2, 3, 5, 8}
4) A ∩ C
A) {1} B) {1, 2, 3, 4, 5, 7, 8, 9}
C) {4, 6, 7, 9} D) {1, 2, 3, 5, 7, 9}
5) (A ∩ B) ∪ C
A) {1, 2, 3, 4, 5, 9} B) {1, 2, 3, 5} C) {1, 2, 3} D) {2, 3, 5}
6) (B ∪ C) ∩ A
A) {1, 2, 3, 5} B) {1, 2, 3, 4, 5, 7, 9} C) { } D) {1, 2, 3}
7) B
A) {0, 1, 4, 6, 8, 9} B) {1, 4, 6, 8, 9} C) {0, 1, 4, 6, 7, 8, 9} D) {0, 1, 4, 6, 9}
8) A ∪ B
A) {0, 4, 6, 9} B) {4, 6, 9} C) {1, 4, 6, 8, 9} D) {1, 2, 3, 5, 7, 8}
9) A ∩ C
A) {0, 2, 3, 4, 5, 6, 7, 8, 9} B) {1}
C) {1, 2, 3, 4, 5, 7, 8, 9} D) {1, 2, 3, 4, 5, 6, 7, 8, 9}
10) B ∩ C
A) {0, 6, 8} B) {6, 8} C) {1, 2, 3, 4, 5, 7, 9} D) { }
2 Classify Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
List all the elements of B that belong to the given set.
1) B = 7, 7, -14, 0, 4
5 , - 5
4 , 2.5
Integers
A) {7, -14, 0} B) {7, 0} C) {7, -14} D) {7, 0, 7}
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2) B = 3, 5, -18, 0, 1
3 , -3, 1.9
Natural numbers
A) {3} B) 3, 0, - 3 C) {3, 0} D) {-18, 0, 3}
3) B = 11, 6, -10, 0, 0
1
Real numbers
A) 11, 6, -10, 0, 0
1 B) {11, -10, 0} C) 11, -10, 0, 0
1 D) 11, -10
4) B = 19, 6, -9, 0, 0
1 , 0.83
Rational numbers
A) 19, -9, 0, 0
1 , 0.83 B) {19, 0} C) { 6} D) 6, 0
1 , 0.83
5) B = 15, 8, -24, 0, 0
8 , 0.96
Irrational numbers
A) { 8} B) { 8, 0.96} C) 8, 0
8 D) 8, 0
8 , 0.96
6) B = {20, 6, -8, 0, 3
8 , - 8
3 , 4.4, 25π, 0.256256256...}
Integers
A) {20, -8, 0} B) {20, 0} C) {20, -8} D) {20, 0, 6}
7) B = {7, 5, -2, 0, 1
4 , -4, 1.7, 5π, 0.525525525...}
Natural numbers
A) {7} B) 7, 0, - 4 C) {7, 0} D) {-2, 0, 7}
8) B = {7, 8, -8, 0, 0
9 , 16, 0.54, -8π, 0.161616...}
Rational numbers
A) 7, -8, 0, 0
9 , 16, 0.54, 0.161616... B) 7, -8, 0, 0
9 , 0.54
C) 7, -8, 0, 0
9 , 0.54, 0.161616... D) 7, -8, 0, 0
9 , 16, 0.54, -8π, 0.161616...
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9) B = {4, 8, -18, 0, 0
3 , , 0.84, -8π, 0.161616...}
Irrational numbers
A) { 8, -8π} B) { 8}
C) 8, 0
3 ,-8π D) { 8, -8π, 0.161616...}
Approximate the number rounded to three decimal places, and truncated to three decimal places.
10) 8.6586
A) 8.659
8.658
B) 8.660
8.658
C) 8.659
8.659
D) 8.658
8.659
11) 1.57142857
A) 1.571
1.571
B) 1.572
1.571
C) 1.571
1.572
D) 1.570
1.572
12) 13
9
A) 1.444
1.444
B) 1.445
1.444
C) 1.444
1.445
D) 1.445
1.445
3 Evaluate Numerical Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the statement using symbols.
1) The sum of 9 and 3 is 12.
A) 9 + 3 = 12 B) 9
3 = 3 C) 9 · 3 = 27 D) 9 - 3 = 6
2) The difference 70 less 14 equals 56.
A) 70 - 14 = 56 B) 70
14 = 5 C) 70 + 14 = 84 D) 70 · 14 = 980
3) The product of 60 and 12 equals 720.
A) 60 · 12 = 720 B) 60
12 = 5 C) 60 + 12 = 72 D) 60 - 12 = 48
4) The quotient 18 divided by 6 is 3.
A) 18
6 = 3 B) 18 · 6 = 108 C) 18 + 6 = 24 D) 18 - 6 = 12
5) The sum of four times x and 5 decreased by 7 is 8.
A) 4x + 5 - 7 = 8 B) 4(x + 5) - 7 = 8 C) 7 - (4x + 5) = 8 D) 4(x + 5 - 7) = 8
6) Three times the difference of x and 8 is -10.
A) 3(x - 8) = -10 B) 3 - x - 8 = -10 C) 3x - 8 = -10 D) 3 + x - 8 = -10
7) The quotient of x and the sum of 5 and x.
A) x
5 + x B) x + 5 + x C) x(5 + x) D) x + 5
x
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Evaluate the expression.
8) -2 - 3 + 7
A) 2 B) -12 C) 8 D) -6
9) 9 + 2
3
A) 29
3 B) 27
3 C) 29
2 D) 27
2
10) 3 · [8(3 - 8) - 6]
A) -138 B) -30 C) -58 D) -34
11) 3 · [5 + 2 · (8 + 2)]
A) 75 B) 210 C) 35 D) 206
12) 9 - (-6 + 2 · 8 - 1)
A) 0 B) 18 C) -2 D) -12
13) 21
36 · 4
7
A) 1
3 B) 3 C) 7
12 D) 9
7
14) 3
5 · 1
4 + 1
8
A) 9
40 B) 3
20 C) 3
40 D) 9
8
15) 1
4 · 10 - 1
5 + 7
A) 189
20 B) 93
10 C) 84
5 D) 14
5
16) 8 + 3
4 + 4
A) 11
8 B) 5
8 C) 11
0 D) 5
0
17) 8 - 2
2 - 8
A) -1 B) 4 C) - 4 D) 6
18) 7
10 + 1
11
A) 87
110 B) 8
21 C) 4
55 D) 29
7
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19) 7
9 - 2
3
A) 1
9 B) 5
27 C) 5
9 D) 1
3
20)
5
6
2
7
A) 35
12 B) 12
35 C) 5
21 D) 21
5
21) 1
3 + 1
5 · 1
9
A) 16
45 B) 8
135 C) 8
5 D) 2
135
4 Work with Properties of Real Numbers
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the Distributive Property to remove the parentheses.
1) 7(x + 9)
A) 7x + 63 B) 7x + 9 C) x + 63 D) 63x
2) 8x(x + 6)
A) 8x2 + 48x B) 8x2 + 6 C) x2 + 48x D) 48x2
3) 2(5x + 8)
A) 10x + 16 B) 7x + 10 C) 10x + 8 D) 26x
4) 4 1
2 x + 1
8
A) 2x + 1
2 B) 2x + 1
4 C) 2x + 1
8 D) 1
2 x + 1
2
5) (x - 11)(x - 2)
A) x2 - 13x + 22 B) x2 + 22x - 13 C) x2 - 14x + 22 D) x2 - 13x - 13
6) (x + 3)(x - 7)
A) x2 - 4x - 21 B) x2 - 21x - 4 C) x2 - 5x - 21 D) x2 - 4x - 4
7) (x + 7)(x - 7)
A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49
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0.2 Algebra Essentials
1 Graph Inequalities
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
On the real number line, label the points with the given coordinates.
1) -9, -7, -5, -3
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
A)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
B)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
C)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
D)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
2) -4.75, -2, 0, 2.25
-5 -4 -3 -2 -1 0 1 2 3 4-5 -4 -3 -2 -1 0 1 2 3 4
A)
-5 -4 -3 -2 -1 0 1 2 3 4-5 -4 -3 -2 -1 0 1 2 3 4
B)
-5 -4 -3 -2 -1 0 1 2 3 4-5 -4 -3 -2 -1 0 1 2 3 4
C)
-5 -4 -3 -2 -1 0 1 2 3 4-5 -4 -3 -2 -1 0 1 2 3 4
D)
-5 -4 -3 -2 -1 0 1 2 3 4-5 -4 -3 -2 -1 0 1 2 3 4
3) 13
4 , - 13
4
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
A)
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
B)
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
C)
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
D)
-4 -3 -2 -1 0 1 2 3 4-4 -3 -2 -1 0 1 2 3 4
Insert <, >, or = to make the statement true.
4) -1 8
A) < B) > C) =
5) -1.9 3.8
A) < B) > C) =
6) -71 -69
A) < B) > C) =
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7) 29 -29
A) > B) < C) =
8) 1
3 0.33
A) > B) < C) =
9) 1.73 3
A) < B) > C) =
10) 3.14 π
A) < B) > C) =
Write the statement as an inequality.
11) z is positive
A) z > 0 B) z < 0 C) z ≤ 0 D) z ≥ 0
12) y is greater than -12
A) y > -12 B) y < -12 C) y ≥ -12 D) y ≤ -12
13) y is greater than or equal to 40
A) y ≥ 40 B) y > 40 C) y < 40 D) y ≤ 40
14) z is less than or equal to 2
A) z ≤ 2 B) z < 2 C) z > 2 D) z = 2
15) x is less than 6
A) x < 6 B) x > 6 C) x ≤ 6 D) x ≥ 6
Graph the numbers on the real number line.
16) x > -5
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
B)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
D)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
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17) x < 4
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
B)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
D)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
18) x ≥ 4
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
B)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
D)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
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19) x ≤ 5
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
A)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
B)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
C)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
D)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
2 Find Distance on the Real Number Line
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the given real number line to compute the distance.
1) Find d(A, B)
-5 -4 -3 -2 -1 0 1 2 3 4 5
AB
-5 -4 -3 -2 -1 0 1 2 3 4 5
AB
A) 6 B) -6 C) 7 D) 5
3 Evaluate Algebraic Expressions
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression using the given values.
1) x + 13y x = 4, y = 3
A) 43 B) 7 C) 55 D) 17
2) -4xy + 7y - 8 x = -5, y = 1
A) 19 B) 27 C) 35 D) -21
3) -10x + y x = -3, y = 3
A) 33 B) -27 C) 0 D) -7
4) 15x - 13y
7 x = 8, y = 5
A) 55
7 B) 107
7 C) 185
7 D) 29
7
5) 15x - 8y
x + 12 x = 8, y = 4
A) 22
5 B) 1
5 C) 1
4 D) 11
2
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6) 5xy + 50
x x = 5, y = 7
A) 45 B) 15 C) 85 D) 10
7) x - y x = -8, y = 7
A) 15 B) 1 C) -15 D) -1
8) x - y x = -7, y = 3
A) 4 B) 10 C) -4 D) -10
9) 6x - 7y x = 6, y = 7
A) 13 B) 85 C) -13 D) -85
10) |x|
x + |y|
y x = 5 and y = -3
A) 0 B) 2 C) 1 D) -1
11) |-8x - 10y| x = 4, y = -1
A) 22 B) 42 C) 32 D) 48
12) 4 x + 5 y x = 5, y = -3
A) 35 B) 5 C) -35 D) -5
Use the formula C = 5
9 (F - 32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of
the Fahrenheit temperature.
13) F = 32°
A) 0° C B) 5° C C) -5° C D) 10° C
Express the statement as an equation involving the indicated variables.
14) The area A of a rectangle is the product of its length l and its width w.
A) A = lw B) A = l + w C) A = 2(l + w) D) A = l
w
15) The perimeter P of a rectangle is twice the sum of its length l and its width w.
A) P = 2(l + w) B) P = l + w C) P = lw D) P = 2lw
16) The circumference C of a circle is the product of π and its diameter d.
A) C = πd B) C = π
d C) C = π + d D) C = 2πd
17) The area A of a triangle is one-half the product of its base b and its height h.
A) A = 1
2 bh B) A = 2bh C) A = 1
2 (b + h) D) A = bh
18) The volume V of a sphere is 4
3 times π times the cube of the radius r.
A) V = 4
3 πr3 B) V = 4
3 πr2 C) V = 4
3 π 3 r D) V = 4
3 πr
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19) The surface area S of a sphere is 4 times π times the square of the radius r.
A) S = 4πr2 B) S = 4πr C) S = 4π r D) S = πr2
20) The volume V of a cube is the cube of the length x of a side.
A) V = x3 B) V = 3 x C) V = 3x D) V = x2
21) The surface area S of a cube is 6 times the square of the length x of a side.
A) S = 6x2 B) S = 6x C) S = 6 + x2 D) S = x2
Solve the problem.
22) The weekly production cost C of manufacturing x calendars is given by C(x) = 20 + 6x, where the variable
C is in dollars. What is the cost of producing 292 calendars?
A) $1772.00 B) $5846.00 C) $1752.00 D) $312.00
23) At the beginning of the month, Christopher had a balance of $208 in his checking account. During the next
month, he wrote a check for $57, deposited $103, and wrote another check for $190. What was his balance
at the end of the month?
A) $64 B) -$64 C) -$142 D) $142
4 Determine the Domain of a Variable
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine which value(s), if any, must be excluded from the domain of the variable in the expression.
1) x2 - 1
x
A) x = 0 B) x = 1, x = -1 C) x = 1, x = 0 D) x = -1
2) 7x - 3
x2 - 81
A) x = 9, x = -9 B) x = 81 C) x = 9 D) x = 3
7
3) x3 + 6x4
x2 + 49
A) x = 0, x = - 1
6 B) x = -49 C) x = -7 D) none
4) x2 + 10x + 3
x3 - 25x
A) x = 5, x = -5, x = 0 B) x = 5, x = -5 C) x = 0 D) x = 5, x = 0
5) x
x - 8
A) x = 8 B) x = -8 C) x = 0 D) none
6) 2
x + 6
A) x = -6 B) x = 6 C) x = 0 D) none
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7) x - 8
x - 6
A) x = 6 B) x = -6 C) x = 0 D) none
5 Use the Laws of Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
1) 34
A) 81 B) 12 C) -81 D) -12
2) -44
A) -256 B) 16 C) 256 D) -16
3) 4-3
A) 1
64 B) -64 C) 64 D) 1
12
4) (-5)-4
A) 1
625 B) -625 C) 625 D) - 1
625
5) -5-2
A) - 1
25 B) -25 C) 25 D) 1
10
6) (-5)3
A) -125 B) 125 C) -15 D) 15
7) 2-7 · 24
A) 1
8 B) 8 C) 4 D) 1
16
8) (2-2)-1
A) 4 B) 1
4 C) 1
2 D) 2
Simplify the expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or
negative, we assume that the base is not 0.
9) (5xy)3
A) 125x3y3 B) 125xy C) 5x3y3 D) 1
125x3y3
10) (9x3)-2
A) 1
81x6 B) 81x6 C) x6
81 D) 81
x6
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11) (-5x3)-1
A) - 1
5x3 B) - 1
125x3 C) 1
5x3 D) 1
125x3
12) (x8y-1)8
A) x64
y8 B) y8
x64 C) 1
x64y8 D) x64y8
13) (x-4y)9
A) y9
x36 B) y9
x4 C) 1
x36y9 D) x36y9
14) x-2y7
xy9
A) 1
x3y2 B) 1
xy2 C) y2
x3 D) x
y2
15) x-3y9
x4y13
A) 1
x7y4 B) x7y4 C) y4
x7 D) x7
y4
16) 7x-1
4y-1
-3
A) 64x3
343y3 B) 343x3
64y3 C) 64y3
343x3 D) 343y3
64x3
17) 6x-1
7y-1
-2
A) 49x2
36y2 B) 36x12
49y12 C) 49y2
36x2 D) 36x2
49y2
18) (x-6y8)-7z4
A) x42z4
y56 B) y56z4
x42 C) x42
y56z4 D) y56
x42z4
19) -8x7y-2
7z7
-2
A) 49y4z14
64x14 B) 64x14
49y4z14 C) 49z14
64x14y4 D) 49y4
64x14z14
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Evaluate the expression using the given value of the variables.
20) (x + 2y)2 for x = 2, y = 2
A) 36 B) 6 C) 12 D) 16
21) 5x-1y2 for x = -1, y = -2
A) - 20 B) - 4
5 C) - 5
4 D) -20
22) 4x2 - 4y2 for x = -3, y = 2
A) 20 B) 28 C) 52 D) -28
23) 4x3 + 5x2 - 5x + 9 for x = 1
A) 13 B) 23 C) 3 D) -5
Solve.
24) What is the value of (6666)4
(2222)4 ?
A) 81 B) (3333)4 C) 162 D) (2222)4
6 Evaluate Square Roots
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
1) 25
A) 5 B) 625 C) 1
25 D) not a real number
2) (-7)2
A) 7 B) 2401 C) 1
49 D) not a real number
Find the value of the expression using the given values.
3) x2 x = -6
A) 6 B) 2 3 C) -6 D) -2 3
4) ( x)2 x = 9
A) 9 B) 81 C) 1
81 D) 1
9
5) x2 + y2 x = 15, y = 20
A) 25 B) 13 C) 18 D) 24
6) x2 + y2 x = -5, y = 2
A) 29 B) 7 C) -3 D) 10
7) x2 + y2 x = 1, y = 2
A) 3 B) -1 C) 5 D) 1
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8) yx x = -3, y = 6
A) 1
216 B) 216 C) -216 D) - 1
216
7 Use a Calculator to Evaluate Exponents
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a calculator to evaluate the expression. Round the answer to three decimal places.
1) (-3.36)-5
A) -0.002 B) 0.002 C) -428.249 D) 428.249
2) -(-4.47)2
A) -19.981 B) 19.981 C) -0.050 D) 0.050
3) (1.08)-6
A) 0.630 B) -0.630 C) -1.587 D) 1.587
8 Use Scientific Notation
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Write the number in scientific notation.
1) 6712
A) 6.712 × 103 B) 6.712 × 104 C) 6.712 × 10-3 D) 6.712 × 101
2) 237.5
A) 2.375 × 102 B) 2.375 × 10-2 C) 2.375 × 101 D) 2.375 × 10-1
3) 210.081
A) 2.10081 × 102 B) 2.10081 × 10-2 C) 2.10081 × 101 D) 2.10081 × 10-1
4) 81,000
A) 8.1 × 104 B) 8.1 × 10-4 C) 8.1 × 105 D) 8.1 × 10-5
5) 3,900,000
A) 3.9 × 106 B) 3.9 × 10-6 C) 3.9 × 105 D) 3.9 × 10-5
6) 0.000862
A) 8.62 ∘ 10-4 B) 8.62 × 104 C) 8.62 × 10-5 D) 8.62 × 10-3
7) 0.000093111
A) 9.3111 × 10-5 B) 9.3111 × 105 C) 9.3111 ± 10-4 D) 9.3111 × 104
8) 0.0000042811
A) 4.2811 × 10-6 B) 4.2811 × 106 C) 4.2811 × 10-5 D) 4.2811 × 10-7
9) 0.00000016107
A) 1.6107 × 10-7 B) 1.6107 × 107 C) 1.6107 × 10-6 D) 1.6107 × 106
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10) 0.0000000487015
A) 4.87015 × 10-8 B) 4.87015 × 108 C) 4.87015 × 10-7 D) 4.87015 × 10-9
11) In a certain city, the subway system carried a total of 1,840,000,000 passengers.
A) 1.84 × 109 B) 18.4 × 109 C) 1.84 × 108 D) 1.84 × 1010
12) A business projects next year's profits to be $884,000,000.
A) 8.84 × 108 B) 8.84 × 107 C) 8.84 × 109 D) 8.84 × 10-9
13) A computer compiles a program in 0.000676 seconds.
A) 6.76 × 10-4 B) 6.76 × 10-5 C) 6.76 × 10-6 D) 6.76 × 103
Write the number as a decimal.
14) 1.70 × 103
A) 1700 B) 17,000 C) 170 D) 51
15) 6.650 × 105
A) 665,000 B) 6,650,000 C) 66,500 D) 332.5
16) 6.2121 × 105
A) 621,210 B) 6,212,100 C) 62,121 D) 310.605
17) 9.54 × 10-4
A) 0.000954 B) 0.00954 C) 0.0000954 D) -954,000
18) 7.987 × 10-5
A) 0.00007987 B) 0.0007987 C) 0.000007987 D) -798,700
19) 3.974 × 10-6
A) 0.000003974 B) 0.00003974 C) 0.0000003974 D) -3,974,000
20) 4.0694 × 10-7
A) 0.00000040694 B) 0.0000040694 C) 0.000000040694 D) -406940,000
21) There are 2.106 × 106 miles of highways, roads, and streets in a certain country.
A) 2,106,000 B) 21,060,000 C) 210,600 D) 210,600,000
0.3 Geometry Essentials
1 Use the Pythagorean Theorem and Its Converse
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The lengths of the legs of a right triangle are given. Find the hypotenuse.
1) a = 4, b = 3
A) 5 B) 7 C) 2 D) 25
2) a = 12, b = 16
A) 20 B) 11 C) 14 D) 19
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The lengths of the sides of a triangle are given. Determine if the triangle is a right triangle. If it is, identify the
hypotenuse.
3) 5, 12, 13
A) right triangle; 13 B) right triangle; 12 C) right triangle; 5 D) not right triangle
4) 2, 3, 4
A) right triangle; 4 B) right triangle; 3 C) right triangle; 2 D) not right triangle
5) 9, 12, 15
A) right triangle; 15 B) right triangle; 12
C) right triangle; 9 D) not a right triangle
6) 15, 36, 39
A) right triangle; 39 B) right triangle; 36
C) right triangle; 15 D) not a right triangle
7) 21, 72, 75
A) right triangle; 75 B) right triangle; 72
C) right triangle; 21 D) not a right triangle
8) 10, 20, 25
A) right triangle; 25 B) right triangle; 20
C) right triangle; 10 D) not a right triangle
9) 6, 8, 12
A) right triangle; 12 B) right triangle; 8
C) right triangle; 6 D) not a right triangle
Solve. Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet.
10) A guard tower at a state prison stands 103 feet tall. How far can a guard see from the top of the tower?
Round to the nearest tenth of a mile.
A) 12.4 mi B) 5600.3 mi C) 17.6 mi D) 909 mi
11) A person who is 3 feet tall is standing on the beach and looks out onto the ocean. Suddenly, a ship
appears on the horizon. How far is the ship from the shore? Round to the nearest tenth of a mile.
A) 2.1 mi B) 5600.3 mi C) 3 mi D) 154.2 mi
2 Know Geometry Formulas
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) Find the area A of a rectangle with length 18 in and width 20 in.
A) A = 360 in2 B) A = 720 in2 C) A = 38 in2 D) A = 72 in2
2) Find the area A of a rectangle with length 7.5 ft and width 10.4 ft.
A) A = 78 ft2 B) A = 156 ft2 C) A = 17.9 ft2 D) A = 30 ft2
3) Find the area A of a triangle with height 3 in and base 3 in.
A) A = 9
2 in2 B) A = 9
2 in C) A = 9 in2 D) A = 9 in
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4) Find the area A and circumference C of a circle of radius 7 in.. Express the answer in terms of π.
A) A = 49π in.2; C = 14π in. B) A = 14π in.2; C = 14π in.
C) A = 196π in.2; C = 7π in. D) A = 28π in.2; C = 7π in.
5) Find the area A and circumference C of a circle of diameter 11 ft. Use 3.14 for π. Round the result to the
nearest tenth.
A) A = 95 ft2; C = 34.5 ft B) A = 34.5 ft2; C = 34.5 ft
C) A = 379.9 ft2; C = 17.3 ft D) A = 69.1 ft2; C = 17.3 ft
6) Find the volume V of a rectangular box with length 8 yd, width 2 yd, and height 6 yd.
A) V = 96 yd3 B) V = 32 yd3 C) V = 72 yd3 D) V = 384 yd3
7) Find the surface area S of a rectangular box with length 3 ft, width 2 ft, and height
4 ft.
A) 52 ft2 B) 40 ft2 C) 26 ft2 D) 44 ft2
8) Find the volume V and surface area S of a sphere of radius 8 centimeters. Express the answer in terms of π.
A) V = 2048
3 π cm3; S = 256π cm2 B) V = 512
3 π cm3; S = 2048
3 π cm2
C) V = 2048π cm3; S = 16π cm2 D) V = 512π cm3; S = 64π cm2
9) Find the volume V of a sphere of radius 2 ft. Use 3.14 for π. If necessary, round the result to the nearest
tenth.
A) V = 33.5 ft3 B) V = 16.7 ft3 C) V = 18.8 ft3 D) V = 267.9 ft3
10) Find the volume V of a right circular cylinder with radius 7 ft and height 16 ft. Express the answer in terms
of π.
A) V = 784π ft3 B) V = 196π ft3 C) V = 112π ft3 D) V = 56π ft3
11) Find the surface area S of a right circular cylinder with radius 7 cm, and height 6 cm. Use 3.14 for π.
Round your answer to one decimal place.
A) 571.4 cm2 B) 285.7 cm2 C) 923.2 cm2 D) 439.6 cm2
12) Find the volume V of a sphere of diameter 8 yd. Use 3.14 for π. If necessary, round the result to the nearest
tenth.
A) V = 267.9 yd3 B) V = 67 yd3 C) V = 150.7 yd3 D) V = 2143.6 yd3
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13) Find the area of the shaded region. Express the answer in terms of π.
9
9
A) 81 - 81
4 π square units B) 324 - 81π square units
C) 81 - 81
2 π square units D) 81
4 π + 81 square units
14) Find the area of the shaded region. Express the answer in terms of π.
1
1
A) 1
2 π square units B) 1
4 π square units C) 1
2 square units D) 1π square units
15) Find the area of the shaded region. Express the answer in terms of π.
2
2
A) 2π - 4 square units B) 1π- 4 square units
C) 4 square units D) 2π- 2 square units
16) A bicycle wheel makes 4 revolutions. Determine how far the bicycle travels in inches if the diameter of the
wheel is 13 in. Use π ≈ 3.14. Round to the nearest tenth.
A) 163.3 in. B) 40.8 in. C) 52 in. D) 326.6 in.
17) A rectangular patio has dimensions 10 feet by 15 feet. The patio is surrounded by a border with a uniform
width of 2 feet. Find the area of the border.
A) 116 ft2 B) 54 ft2 C) 158 ft2 D) 84 ft2
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18) A circular swimming pool, 20 feet in diameter, is enclosed by a circular deck that is 4 feet wide. What is the
area of the deck? Use π = 3.1416.
A) 301.6 ft2 B) 584.3 ft2 C) 703.7 ft2 D) 314.2 ft2
19) Find the perimeter. Approximate the result to the nearest tenth using 3.14 for π.
9 ft
4 ft
A) 28.3 ft B) 34.6 ft C) 32.3 ft D) 38.6 ft
20) Find the area of the window. Approximate the result to the nearest tenth using 3.14 for π.
8 dm
3 dm
A) 27.5 dm2 B) 52.3 dm2 C) 38.1 dm2 D) 26.4 dm2
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3 Understand Congruent Triangles and Similar Triangles
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The triangles are similar. Find the missing length x and the missing angles A, B, C.
1)
92°
16 28
39° 49°
14
A) x = 8 units; A = 92°; B = 39°; C = 49° B) x = 16 units; A = 39°; B = 92°; C = 49°
C) x = 8 units; A = 49°; B = 39°; C = 92° D) x = 16 units; A = 92°; B = 39°; C = 49°
2)
14°
27°
30
10
20
139°
A) x = 15; A = 27; B = 14; C = 139 B) x = 30; A = 14; B = 27; C = 139
C) x = 15; A = 139; B = 14; C = 27 D) x = 30; A = 27; B = 14; C = 139
Solve. If necessary, round to the nearest tenth.
3) A flagpole casts a shadow of 33 feet. Nearby, a 5-foot tree casts a shadow of 2 feet. What is the height of
the flagpole?
A) 82.5 ft B) 13.2 ft C) 0.3 ft D) 330 ft
4) If a flagpole 27 feet tall casts a shadow that is 36 feet long, find the length of the shadow cast by an antenna
which is 18 feet tall.
A) 24 ft B) 13.5 ft C) 54 ft D) 27 ft
5) The zoo has hired a landscape architect to design the triangular lobby of the children's petting zoo. In his
scale drawing, the longest side of the lobby is 6 cm. The shortest side of the lobby is 2 cm. The longest side
of the actual lobby will be 49 m. How long will the shortest side of the actual lobby be?
A) 16.3 m B) 0.2 m C) 147 m D) 1.5 m
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6) If a tree 32.5 feet tall casts a shadow that is 13 feet long, find the height of a tree casting a shadow that is 25
feet long.
A) 62.5 ft B) 10 ft C) 16.9 ft D) 44.5 ft
0.4 Polynomials
1 Recognize Monomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Tell whether the expression is a monomial. If it is, name the variable(s) and coefficient, and give the degree of the
monomial.
1) -18x
A) Monomial; variable x; coefficient -18; degree 1
B) Monomial, variable x; coefficient 1; degree -18
C) Monomial,; variable x; coefficient -18; degree 0
D) Not a monomial
2) 13x4
A) Monomial; variable x; coefficient 13; degree 4 B) Monomial; variable x; coefficient 4; degree 13
C) Monomial; variable x; coefficient 4; degree 0 D) Not a monomial
3) 7
x
A) Monomial; variable x; coefficient 7; degree 1 B) Monomial; variable x; coefficient 7; degree -1
C) Monomial; variable x; coefficient 7; degree 0 D) Not a monomial
4) -11x-3
A) Monomial; variable x; coefficient -11; degree -3
B) Monomial; variable x; coefficient 3; degree -11
C) Monomial; variable x; coefficient -11; degree 3
D) Not a monomial
5) -3xy7
A) Monomial; variables x, y; coefficient -3; degree 8
B) Monomial; variables x, y; coefficient -3; degree 7
C) Monomial; variables x, y; coefficient -3; degree 1
D) Not a monomial
6) 7x2y6
A) Monomial; variables x, y; coefficient 7; degree 8
B) Monomial; variables x, y; coefficient 7; degree 2
C) Monomial; variables x, y; coefficient 7; degree 6
D) Not a monomial
7) 20x
y
A) Monomial; variables x, y; coefficient 20; degree 1
B) Monomial; variables x, y; coefficient 20; degree -2
C) Monomial; variables x, y; coefficient 20; degree 2
D) Not a monomial
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8) - -3x7
y3
A) Monomial; variables x, y; coefficient -3; degree 7
B) Monomial; variables x, y; coefficient -3; degree 3
C) Monomial; variables x, y; coefficient -3; degree 4
D) Not a monomial
9) 4x3 - 5
A) Monomial; variable x; coefficient 4; degree 3 B) Monomial; variable x; coefficient 5 ; degree 3
C) Monomial; variable x; coefficient 4; degree 1 D) Not a monomial
2 Recognize Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Tell whether the expression is a polynomial. If it is, give its degree.
1) 7x5 - 2
A) Polynomial; degree 5 B) Polynomial; degree 2
C) Polynomial; degree 7 D) Not a polynomial
2) 1 - 5x
A) Polynomial; degree 1 B) Polynomial; degree 5
C) Polynomial; degree -5 D) Not a polynomial
3) 18
A) Polynomial, degree 0 B) Polynomial, degree 1
C) Polynomial, degree 18 D) Not a polynomial
4) 7π
A) polynomial, degree 0 B) polynomial, degree 1
C) polynomial, degree 7 D) not a polynomial
5) 7x5 - 2
x
A) Polynomial; degree 5 B) Polynomial; degree -1
C) Polynomial; degree 1 D) Not a polynomial
6) 14
x + 1
A) Polynomial, degree 0 B) Polynomial, degree -1
C) Polynomial, degree 14 D) Not a Polynomial
7) -6y8 - 3
A) Polynomial; degree 8 B) Polynomial; degree -6
C) Polynomial; degree 3 D) Not a polynomial
8) 8z3 + z
A) Polynomial; degree 3 B) Polynomial; degree 4
C) Polynomial; degree 1 D) Not a polynomial
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9) -6x6 - 18x4
-3x2
A) Polynomial; degree 4 B) Polynomial; degree 6
C) Polynomial; degree 0 D) Not a polynomial
3 Add and Subtract Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Add or subtract as indicated. Express the answer as a single polynomial in standard form.
1) (8x2 + 3x - 13) + (6x + 13)
A) 8x2 + 9x B) 8x2 + 9x - 26 C) 8x2 + 3x + 26 D) 17x3
2) (8x2 - 6x - 5) + (8x2 + 8x - 3)
A) 16x2 + 2x - 8 B) 3x2 + 16x - 9 C) 16x2 - 2x - 8 D) 16x2 + 2x + 8
3) (8x2 + 14x - 6) - (3x2 + 9x - 18)
A) 5x2 + 5x + 12 B) 5x2 + 17x - 24 C) 5x2 + 5x - 24 D) 5x2 + 5x - 12
4) (7x4 - 8x3) + (2x4 - 5x3)
A) 9x4 - 13x3 B) 9x8 - 13x6 C) -4x7 D) -4x14
5) (17x5 - 18x4) - (9x5 - 14x4)
A) 8x5 - 4x4 B) 8x5 - 32x4 C) 4x9 D) 26x5 - 32x4
6) (4x7 + 4x6) + (3x7 - 8x6 + 2)
A) 7x7 - 4x6 + 2 B) -4x7 - 4x6 + 2x C) 2x - 4x7 - 5x6 D) -2x14
7) (-9x2 - 10) - (-x3 + 6x2 + 1)
A) x3 - 15x2 - 11 B) -8x3 - 4x2 - 1 C) x3 - 3x2 - 9 D) -8x3 + 6x2 - 11
8) (9x5 - 12x2 - 14) - (4x5 - 7x2 + 6)
A) 5x5 - 5x2 - 20 B) 5x5 - 8x2 - 8 C) 5x5 - 5x2 - 8 D) -20x7
9) (8x7 + 9x6 - 12) - (-11x6 + 6x7 - 20)
A) 2x7 + 20x6 + 8 B) 2x7 + 15x6 - 32 C) 2x7 + 20x6 - 32 D) 30x13
10) (6x5 - 6x2 - 7x) + (2x5 - 2x2 - 5x)
A) 8x5 - 8x2 - 12x B) -5x5 + 4x2 - 11x C) 8x - 8x5 - 12x2 D) -12x8
11) -3(x2 + 3x + 1) + (-3x2 - x + 5)
A) -6x2 - 10x + 2 B) 0x2 - 10x + 2 C) -6x2 - 9x + 2 D) -6x2 - 10x + 6
12) 4(-4x3 + x2 - 1) - 5(6x3 + 2x + 2)
A) -46x3 + 4x2 - 10x - 14 B) -46x3 + 4x2 + 10x - 14
C) -46x3 + x2 - 10x - 14 D) -46x3 + 4x2 - 10x + 14
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13) (x2 + 1) - (9x2 + 5) + (x2 + x - 2)
A) -7x2 + x - 6 B) -9x2 + x - 6 C) -8x2 + x - 6 D) -7x2 + 6x - 1
14) -9(1 - y3) - 3(1 + y + y2 + y3)
A) 6y3 - 3y2 - 3y - 12 B) 6y3 + 3y2 - 3y + 12
C) 6y3 - 3 - ay2 - 3y - 12 D) -6y3 - 3y2 - 3y - 12
4 Multiply Polynomials
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operations. Express the answer as a single polynomial in standard form.
1) 10x(-2x + 6)
A) -20x2 + 60x B) 40x2 C) -20x2 + 6x D) -2x2 + 60x
2) -6x4(12x + 9)
A) -72x5 - 54x4 B) -72x - 54 C) -72x5 + 9 D) -126x4
3) -5x3(4x6 - 11)
A) -20x9 + 55x3 B) -20x6 + 55 C) -20x9 - 11 D) 35x3
4) 3x6(-4x5 + 12x4 + 5)
A) -12x11 + 36x10 + 15x6 B) -12x11 + 36x10
C) -12x11 + 12x4 + 5 D) -12x5 + 36x4 + 15
5) (x - 11)(x2 + 6x - 4)
A) x3 - 5x2 - 70x + 44 B) x3 + 17x2 + 62x - 44
C) x3 - 5x2 - 62x - 44 D) x3 + 17x2 + 70x + 44
6) (10y + 11)(2y2 - 2y - 7)
A) 20y3 + 2y2 - 92y - 77 B) 20y3 - 20y2 - 70y + 11
C) 42y2 - 42y - 147 D) 20y3 + 42y2 + 92y + 77
Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form.
7) (x + 9)(x + 3)
A) x2 + 12x + 27 B) x2 + 27x + 12 C) x2 + 11x + 27 D) x2 + 12x + 12
8) (-2x - 11)(x + 3)
A) -2x2 - 17x - 33 B) -2x2 - 33x - 17 C) -2x2 - 17x - 17 D) -2x2 - 19x - 33
9) (3x + 5)(5x + 9)
A) 15x2 + 52x + 45 B) 8x2 + 52x + 45 C) 15x2 + 52x + 52 D) 8x2 + 52x + 52
10) (x - 3y)(x + 11y)
A) x2 + 8xy - 33y2 B) x + 8xy - 33y C) x2 + 8xy + 8y2 D) x2 + 5xy - 33y2
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11) (x - 9y)(3x - 12y)
A) 3x2 - 39xy + 108y2 B) x2 - 39xy + 108y2
C) 3x2 - 39xy - 39y2 D) x2 - 39xy - 39y2
12) (3x + 6y)(-5x - 12y)
A) -15x2 - 66xy - 72y2 B) -15x2 - 30xy - 72y2
C) -15x2 - 36xy - 72y2 D) -15x2 - 66xy - 66y2
5 Know Formulas for Special Products
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Multiply the polynomials. Express the answer as a single polynomial in standard form.
1) (x + 10)(x - 10)
A) x2 - 100 B) x2 - 20 C) x2 - 20x - 100 D) x2 + 20x - 100
2) (10x + 13)(10x - 13)
A) 100x2 - 169 B) x2 - 169
C) 100x2 - 260x - 169 D) 100x2 + 260x - 169
3) (x + 16)2
A) x2 + 32x + 256 B) x2 + 256 C) 256x2 + 32x + 256 D) x + 256
4) (x - 16)2
A) x2 - 32x + 256 B) x2 + 256 C) 256x2 - 32x + 256 D) x + 256
5) (5x + 12)2
A) 25x2 + 120x + 144 B) 25x2 + 144 C) 5x2 + 120x + 144 D) 5x2 + 144
6) (x + 9y)(x - 9y)
A) x2 - 81y2 B) x2 - 18y2 C) x2 - 18xy - 81y2 D) x2 + 18xy - 81y2
7) (12y + x)(12y - x)
A) 144y2 - x2 B) 24y2 - x2 C) 144y2 - 24xy - x2 D) 144y2 + 24xy - x2
8) (7x - 6)2
A) 49x2 - 84x + 36 B) 49x2 + 36 C) 7x2 - 84x + 36 D) 7x2 + 36
9) (a - b)2
A) a2 - 2ab + b2 B) a2 - ab + b2 C) a2 - 2ab - b2 D) a2 + 2ab + b2
10) (2x + 9y)2
A) 4x2 + 36xy + 81y2 B) 4x2 + 81y2 C) 2x2 + 36xy + 81y2 D) 2x2 + 81y2
11) (6x - 5y)2
A) 36x2 - 60xy + 25y2 B) 36x2 + 25y2
C) 6x2 - 60xy + 25y2 D) 6x2 + 25y2
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12) (x + 3)3
A) x3 + 9x2 + 27x + 27 B) x3 + 3x2 + 3x + 27
C) x3 + 9x2 + 3x + 27 D) x3 + 9x2 + 9x + 27
13) (2x + 3)3
A) 8x3 + 36x2 + 54x + 27 B) 8x3 + 36x2 + 36x + 27
C) 4x6 + 6x3 + 729 D) 4x2 + 12x + 9
6 Divide Polynomials Using Long Division
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the quotient and the remainder.
1) 18x7 - 30x3 divided by 6x
A) 3x6 - 5x2; remainder 0 B) 18x6 - 30x2; remainder 0
C) 3x8 - 5x4; remainder 0 D) 3x7 - 5x3; remainder 0
2) 32x2 + 20x - 13 divided by 4x
A) 8x + 5; remainder -13 B) 8x2 + 5x - 13
4 ; remainder 0
C) 32x + 20; remainder -13 D) 8x - 8; remainder 0
3) x2 + 8x + 12 divided by x + 6
A) x + 2; remainder 0 B) x - 6; remainder 0
C) x2 + 2; remainder 0 D) x3 - 6; remainder 0
4) 2x2 + 7x - 72 divided by x + 8
A) 2x - 9; remainder 0 B) 2x + 9; remainder 0
C) x - 9; remainder 0 D) 2x - 9; remainder 2
5) x2 + 5x - 30 divided by x + 9
A) x - 4; remainder 6 B) x - 4; remainder 0 C) x + 4; remainder 6 D) x - 6; remainder 4
6) x2 + 11x + 22 divided by x + 5
A) x + 6; remainder -8 B) x + 6; remainder 8
C) x + 6; remainder 0 D) x + 7; remainder 0
7) 9x3 + 61x2 - 5x + 63 divided by x + 7
A) 9x2 - 2x + 9; remainder 0 B) 9x2 + 2x + 9; remainder 0
C) x2 + 3x + 4; remainder 0 D) x2 + 2x + 9; remainder 0
8) 20x3 + 41x2 - 5x - 8 divided by -5x - 4
A) -4x2 - 5x + 5; remainder 12 B) -4x2 - 5x + 5; remainder 0
C) -4x2 - 5x + 5; remainder 15 D) x2 + 5; remainder -5
9) 5x3 - 7x2 + 7x - 8 divided by 5x - 2
A) x2 - x + 1; remainder -6 B) x2 - x + 1; remainder 6
C) x2 - x + 1; remainder 10 D) x2 + x -1; remainder -6
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10) x4 + 256 divided by x - 4
A) x3 + 4x2 + 16x + 64; remainder 512 B) x3 + 4x2 + 16x + 64; remainder 256
C) x3 + 4x2 + 16x + 64; remainder 0 D) x3 - 4x2 + 16x - 64; remainder 512
11) -10x3 - 15x2 + 23x + 15 divided by -2x - 5
A) 5x2 - 5x + 1; remainder 20 B) 5x2 - 5x + 1; remainder 0
C) 5x2 - 5x + 1; remainder 23 D) x2 + 1; remainder -5
12) 9x3 + 24x2 + 3x - 13 divided by -3x - 5
A) -3x2 - 3x + 4; remainder 7 B) -3x2 - 3x + 4; remainder 0
C) -3x2 - 3x + 4; remainder 10 D) x2 + 4; remainder -3
13) x4 + 4x2 + 5 divided by x2 + 1
A) x2 + 3; remainder 2 B) x2 + 3x + 1
2 ; remainder 0
C) x2 + 3; remainder 0 D) x2 + 3x + 1; remainder 2
14) x4 + 256 divided by x - 4
A) x3 + 4x2 + 16x + 64; remainder 512 B) x3 + 4x2 + 16x + 64; remainder 256
C) x3 + 4x2 + 16x + 64; remainder 0 D) x3 - 4x2 + 16x - 64; remainder 512
15) x2 - 16a2 divided by x - 4a
A) x + 4a B) x - 4a C) x2 - 8xa D) x2 + 8xa
7 Work with Polynomials in Two Variables
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Multiply the polynomials using the FOIL method. Express the answer as a single polynomial in standard form.
1) (x - 2y)(x + 9y)
A) x2 + 7xy - 18y2 B) x + 7xy - 18y C) x2 + 7xy + 7y2 D) x2 + 4xy - 18y2
2) (-3x + 7y)(-3x - 4y)
A) 9x2 - 9xy - 28y2 B) 9x2 - 21xy - 28y2 C) 9x2 + 12xy - 28y2 D) 9x2 - 9xy - 9y2
Multiply the polynomials using the special product formulas. Express the answer as a single polynomial in
standard form.
3) (x + 3y)(x - 3y)
A) x2 - 9y2 B) x2 - 6y2 C) x2 - 6xy - 9y2 D) x2 + 6xy - 9y2
4) (6x + y)(6x - y)
A) 36x2 - y2 B) 12x2 - y2 C) 36x2 - 12xy - y2 D) 36x2 + 12xy - y2
5) (5x + 9y)(5x - 9y)
A) 25x2 - 81y2 B) 25x2 - 90xy - 81y2
C) 10x2 - 18y2 D) 25x2 + 90xy - 81y2
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6) (x - y)2
A) x2 - 2xy + y2 B) x2 - xy + y2 C) x2 - y2 D) x2 - 2x2y2 + y2
7) (x - 3y)2
A) x2 - 6xy + 9y2 B) x2 - 3xy + 9y2 C) x2 - y2 D) x2 + 6xy + 9y2
8) (4x - y)2
A) 16x2 - 8xy + y2 B) 16x2 - 4xy + y2 C) 16x2 + y2 D) 16x2 - 8xy - 2y2
9) (2x + 7y)2
A) 4x2 + 28xy + 49y2 B) 4x2 + 49y2 C) 2x2 + 28xy + 49y2 D) 2x2 + 49y2
10) (10x - 11y)2
A) 100x2 - 220xy + 121y2 B) 100x2 + 121y2
C) 10x2 - 220xy + 121y2 D) 10x2 + 121y2
0.5 Factoring Polynomials
1 Factor the Difference of Two Squares and the Sum and Difference of Two Cubes
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Factor the polynomial by removing the common monomial factor.
1) 6x - 54
A) 6(x - 9) B) 6(x + 9) C) x(x - 6) D) x(x + 6)
2) 4x2 - 8x
A) 4x(x - 2) B) 4x(x + 2) C) 4(x2 - 2x) D) 4x2(x - 2)
Factor the difference of two squares.
3) x2 - 9
A) (x + 3)(x - 3) B) (x + 9)(x - 9) C) (x - 3)(x - 3) D) (x2 + 3)(x2 - 3)
4) 100x2 - 1
A) (10x - 1)(10x + 1) B) (10x + 1)2 C) (10x - 1)2 D) prime
5) 16 - x2
A) (4 - x)(4 + x) B) (4 + x)2 C) (4 - x)2 D) prime
6) 9x2 - 49
A) (3x + 7)(3x - 7) B) (3x - 7)2 C) (3x + 7)2 D) (9x + 1)(x - 49)
Factor the sum or difference of two cubes.
7) x3 - 64
A) (x - 4)(x2 + 4x + 16) B) (x + 4)(x2 - 4x + 16)
C) (x - 4)(x2 + 16) D) (x + 64)(x2 - 1)
8) x3 + 27
A) (x + 3)(x2 - 3x + 9) B) (x - 3)(x2 + 3x + 9) C) (x + 3)(x2 + 9) D) (x - 27)(x2 - 1)
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