Solution Manual for Intermediate Algebra 12th edition
Lial Hornsby and McGinnis 0321969359
9780321969354
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Decide whether the expression has been simplified correctly.
1) (ab)8 = a8b8
a
B)
A) No B) Yes Answer: A 3) (4b)9
A) Yes B) No Answer: A 4) (9b)8
9b8 A) Yes B) No Answer: B 5) x7 x9 = x16 A) No B) Yes Answer: B 6) x6 x9 = x54 A) No B) Yes Answer: A 7) xy0 = x A) Yes B) No Answer: A 8) a 9 3 3 = 93 A) No B) Yes Answer: B
A) No
Yes Answer: B 2) (ab)5 = ab5
= 49b9
=
A) No B) Yes
Answer: A
Apply the product rule for exponents, if possible.
10) x7 x2
A) x10
Answer: D
B) x14
C) x7
D) x9
2 a 9) a 3 4 4 = 3
Write the expression with only positive exponents. Assume all variables represent nonzero numbers. Simplify if necessary.
3 11)
y2 A) y13 B) y11 C) y9 D) y36 Answer: B 12) (-3x5y)(-4x9y2) A) 12x14y3 B) 12x15y3 C) 12x45y2 D) -12x14y2 Answer: A 13) (-2x3)(9x10y6) A) -18x30y9 B) -18x13y6 C) -18x30y6 D) 18x13y6 Answer: B 14) g10 h2 A) g20h B) The product rule does not apply. C) gh8 D) gh12 Answer: B Evaluate
expression. 15) 60 A) 0 B) -1 C) 1 D) 6 Answer: C 16) -40 A) -1 B) -4 C) 0 D) 1 Answer: A 17) (-7)0 A) 1 B) 0 C) -1 D) -7 Answer: A 18) 80 + 30 A) 11 B) 0 C) 2 D) 1 Answer: C 19) (-13)0 + (-9)0 A) 0 B) -22 C) -2 D) 2 Answer: D
y3 y6
the
20) r -7 A) 1 r7 Answer: A B) -r7 C)1 r7 D) r1/7
4 20 B) 3 C)1 D)3 3 20 6 20 21) 9-2 A) -91/2 B)1 92 C) -92 D) 1 92 Answer: D 22) (4p)-2 A) 1 16p2 Answer: A 23) 3x-3 A) 1 27x3 Answer: C B) 1 8p-2 B) 1 3x3 C) 1 -8p2 C) 3 x3 D) 1 4p2 D) -9x 24) (-a)-4 A) 1 -a4 Answer: D 25) 10-1 - 4-1 A)B) 1 a -4 C) 4a D) 1 a4 Answer: D Evaluate the expression. 26) 2-3 7-4 A) 8 2401 Answer: C 27) 1 -4-2 B) 16,807 16 C) 2401 8 D) 16 16,807 A) -4 B) -16 C) 16 D) 4 Answer: B 28) 1 9-4 A) 729 B) 36 C) 6561 D) 59,049 Answer: C
Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers.
5 29) 2 5 -4 A)625 16 B) 16 625 C) 625 16 D)16 625 Answer: C 30) 5 2 -3 A) 8 125 B)125 8 C) 125 8 D)8 125 Answer: A
31) x14 x5 A) x9 B) -x9 C) 1 x9 D) x19 Answer: A 32) x4 x15 A) 1 x11 Answer: A 33) x -18 x -9 A) 1 x9 Answer: A 34) x -7 x -17 B) 1 x19 B) 1 x27 C) x11 D) -x11 C) -x27 D) x9 A) 1 x24 Answer: C 35) x -8 x -8 B) -x10 C) x10 D) 1 x10
6 A) x16 B) 1 x16 C) 1 D) -x8
Answer: C
A) 1
B) The quotient rule does not apply. C) 92 D) 9
C
C) The quotient rule does not apply.
Answer: C
Simplify the expression. Write your answer with only positive exponents. Assume that all variables represent nonzero real numbers.
Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
7
4
)
36) 9 9-1
Answer:
37) x3 y7 A) x y4 B) x4
D)
1 y4
38) (x3
3 A) 1 x9 Answer: A 39) 7 2 3 B) 1 x6 C) x6 D) x9 A) 7 3 Answer: B B) 49 9 C)7 9 D) 9 49 40) -2w7 x A) 16w28 x4 Answer: A B) -16w28 x C) 16w11 x4 D) -16w28 x4
-
41) m
10m5m
1 A) m8 B) 1 m6 C) m6 D) 1 m5 Answer: B
-
-
8 ) 42) (k-6 7k6 A) k48 B) 1 k36 C) 1 k7 D) k36 Answer: B
9 ) ) ) ) ) ) -2 5 43) (3-2 7-4 -3 A) 1 36 76 Answer: D B) 36 76 C) 1 36 712 D) 36 712 44) (72 65 -3 A) 77 67 B) 76 615 C) 1 77 67 D) 1 76 615 Answer: D 45) (3x-5 2(x2 -4 A) 1 3-10x18 Answer: B B) 32 x18 C) 32x80 D) 32 x5 46) (x-4y5 -2 A) 1 x8y10 Answer: D 47) 18r4(r3) 7(r-2 5 A) 18r2 7 Answer: D B) y3 x -6 B) 18 7r8 C) x -6 y3 C) 18 7r2 D) x8 y10 D) 18r8 7 48) 10t-4 t2 -4 11 t-4 A) 11t18 104 Answer: D B) 11t24 104 C) 11 10t28 D) 11t28 104 49) 3x4y3 9xy2 A) x8y6 3 Answer: C B) x19y13 3 C) 27x19y13 D) 27x8y6
10 -2 50) 2x3y-3 x -5y4 A) y14 2x16 Answer: C B) 2x16 y14 C) y14 4x16 D) y14 2x8 Express the number in scientific notation. 51) 501,916 A) 5.01916 × 106 B) 5.01916 × 105 C) 5.01916 × 101 D) 5.01916 × 10-5 Answer: B 52) 844.6 A) 8.446 × 103 B) 8.446 × 102 C) 8.446 × 10-3 D) 8.446 × 10-2 Answer: B 53) 787.865 A) 7.87865 × 103 B) 7.87865 × 10-2 C) 7.87865 × 102 D) 7.87865 × 10-3 Answer: C 54) -470,000 A) -4.7 × 106 B) -4.7 × 10-6 C) -4.7 × 10-5 D) -4.7 × 105 Answer: D 55) -3,100,000 A) -3.1 × 10-6 B) -3.1 × 105 C) -3.1 × 106 D) -3.1 × 10-5 Answer: C 56) 0.000489 A) 4.89 × 104 B) 4.89 × 10-4 C) 4.89 × 10-3 D) 4.89 × 10-5 Answer: B 57) 0.000019812 A) 1.9812 × 105 B) 1.9812 × 10-5 C) 1.9812 × 10-4 D) 1.9812 × 104 Answer: B 58) 0.0000049312 A) 4.9312 × 10-7 B) 4.9312 × 10-5 C) 4.9312 × 106 D) 4.9312 × 106 Answer: D 59) 0.000000752011 A) 7.52011 × 10-6 B) 7.52011 × 10-7 C) 7.52011 × 106 D) 7.52011 × 107
11 Answer: B 60) 0.000000093809 A) 9.3809 × 10-9 B) 9.3809 × 10-7 C) 9.3809 × 10-8 D) 9.3809 × 108 Answer: C
12
the number in standard notation. 61) 8.59 × 106 A) 515.4 Answer: C B) 859,000 C) 8,590,000 D) 85,900,000 62) 1.527 × 104 A) 15,270 B) 1527 C) 152,700 D) 61.08 Answer: A 63) 1.2387 × 106 A) 74.322 B) 123,870 C) 12,387,000 D) 1,238,700 Answer: D 64) 4.14 × 10-4 A) 0.000414 B) 0.0000414 C) 0.00414 D) -414,000 Answer: A 65) 3.403 × 10-5 A) -340,300 B) 0.000003403 C) 0.0003403 D) 0.00003403 Answer: D 66) 2 713 × 10-6 A) 0.0000002713 B) -2,713,000 C) 0.00002713 D) 0.000002713 Answer: D 67) 7 0151 × 10-7 A) 0.00000070151 B) -701,510,000 C) 0.0000070151 D) 0.000000070151 Answer: A 68) -7.042 x 104 A) -704,200 B) -7,042,000 C) -70,420 D) -7042 Answer: C Find the value of the expression. 69) 0.06× 200,000 400,000 A) 0.03 B) 0.003 C) 0.3 D) 3,000,000 Answer: A 70) 120,000× 0.09 5400 A) 20 B) 2 C) 0.2 D) 20,000 Answer: B
Express
71) 240,000× 0.0003 0.008 × 150,000
9× 105
10-3 8 ×
Solve the problem. Express your answer in scientific notation, rounding as needed 74) The national debt of a small country is $6,400,000,000 and the population is 2,315,000. What is the amount of debt per person?
× 104
75) The earth is approximately 92,900,000 miles from the sun. If 1 mile = 1.61 × 103 m, what is the distance to the sun in meters?
76) The distance from the earth to the sun is 92,900,000 miles. How long would it take a rocket, traveling at 2.9 × 103 miles per hour, to reach the sun?
77) If the speed of light is 3.00 × 108 m/sec, how long does it take light to travel 2.29 × 1011 m, the distance from the sun to Mars?
78) A computer can do one calculation in 1 4 × 10-7 seconds How long would it take the computer to do a trillion ( 1012) calculations?
79) Assume that the volume of the earth is 5 × 1014 cubic meters and the volume of a bacterium is 2.5 × 10-16 cubic meters If the earth could be filled with bacteria, how many would it contain?
× 1031 bacteria
× 1030 bacteria
× 10-31 bacteria
× 10-30 bacteria
13
A) 0.6 B) 0.006 C) 6 D) 0.06 Answer: D 72)
A) -3000 B) 3000 C) -0.003 D) 0.003 Answer:
A) -0.0000025 B) 0.0000025 C) -25,000 D) 25,000 Answer:
3 × 108
D 73) 2×
102
B
A)
B) $2.76
C) $2.76 ×
D) $2.76 ×
Answer:
$2.76 × 102
106
103
D
A) 1.50 × 1010 m B) 5.7 × 1010 m C) 5.7 × 10-10 m D) 1.50 × 1011 m Answer: D
A) 3.2 × 103 hr B) 3.2 × 105 hr C) 3.2 × 102 hr D) 3.2 × 104 hr Answer: D
A) 7.6 × 102 sec B) 7.6 × 103 sec C) 7.6 ×
min D) 76 sec Answer:
102
A
A) 1.4
B) 1.4 ×
C) 1.4 ×
D) 1.4 ×
Answer:
× 10-7 sec
105 sec
1012 sec
106 sec
B
A) 5.0
B) 5.0
C) 2.0
D) 2.0
14 Answer: C
Find the result that a calculator will give for the stated problem. Write your answer using the usual scientific notation.
80) (1.7E13)∗(3E-7)
Answer: B
81) (6.6E13)/(3E-5)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question Provide an appropriate response.
82) For what values, if any, of x (x ≠ 0) and n will x -n be a negative number?
Answer: If x is negative and n is odd, the answer will be negative.
83) If x ≠ 0, explain the simplification of x xn
Answer: The rule for dividing numbers with the same base is to subtract exponents Therefore, the answer is x2n.
84) Simplify the expressions (2x)0 and (2x0) and explain how you arrived at your answers.
Answer: (2x)0 = 1, because the exponent is applied to the entire quantity in the parentheses (2x0) = 2 because the exponent is applied only to the x.
85) Given that 0 < x < 1 and xn = y, explain why as n becomes larger, y becomes closer to 0.
Answer: Answers may vary. One possibility: Since 0 < x < 1, it can be rewritten as 1 , where a > 1. Thus, xn = 1 n a a
= 1 As n becomes larger, the denominator becomes larger, and thus the expression becomes closer to an 0. Therefore, as n becomes larger, xn (or y) becomes closer to 0.
86) Given that n is a positive or negative integer, explain how to convert 8.125 × 10n to standard notation
Answer: If n is positive, move the decimal point to the right n places If n is negative, move the decimal point to the left n places.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Write the polynomial in descending powers of the variable.
87) 5x - 2x3 + 6x2 A) -2x3 + 6x2 + 5x B) 6x2 - 2x3 + 5x
Answer: A
88) 20 - 2z2 + 7z - 12z4
20 - 12z4 + 7z - 2z2
6x2 + 5x - 2x3
5x + 6x2 - 2x3
15 3n
A)
B) 5.1 × 106 C) 5.1 × 10-6 D) 5.1 × 107
-5.1 × 106
A) 2.2 × 1018 B) 2.2 × 108 C) 19.8 × 1018 D) 2.2 × 10-18
Answer: A
C)
D)
A)
B) -12z4 - 2z2 + 7z + 20
16 C) 10z4 + 2z2 - 7z - 20 D) 20 + 7z - 2z2 - 10z4
B
Answer:
89) -40 - x8 - 24x3 + 48x
A) 48x - 40 - 24x3 - x8
C) x8 + 24x3 - 48x - 40
Answer: D
Give the numerical coefficient and the degree of the term.
90) x
A) Coefficient: 0; degree: 1
C) Coefficient: 1; degree: 0
Answer: D
91) 5z
A) Coefficient: 5; degree: 1
C) Coefficient: 0; degree: 5
Answer: A
92) 5z3
A) Coefficient: 5; degree: 1
C) Coefficient: 1; degree: 5
Answer: D
93) -10z2
A) Coefficient: 2; degree: 10
B) -40 + 48x - 24x3 - x8
D) -x8 - 24x3 + 48x - 40
B) Coefficient: 0; degree: 0
D) Coefficient: 1; degree: 1
B) Coefficient: 5; degree: 0
D) Coefficient: 1; degree: 5
B) Coefficient: 3; degree: 5
D) Coefficient: 5; degree: 3
B) Coefficient: 10; degree: 2
C) Coefficient: 1; degree: 10 D) Coefficient: -10; degree: 2
Answer: D
94) 11
A) Coefficient: 0; degree: 11
C) Coefficient: 11; degree: 0
Answer: C
95) -mn5
A) Coefficient: -1; degree: 6
B) Coefficient: 1; degree: 0
D) Coefficient: 1; degree: 1
B) Coefficient: -m; degree: 5
C) Coefficient: -1; degree: 5 D) Coefficient: -m; degree: 6
Answer: A
96) 10a5b2
A) Coefficient: 10; degree: 7
B) Coefficient: 1; degree: 7
C) Coefficient: 10; degree: 5 D) Coefficient: 1; degree: 8
Answer: A
Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree.
97) 12x2
A) Binomial; 0 B) Binomial; 12
C) Monomial; 2 D) Monomial; 12
Answer: C
17
98) 13x
A) Binomial; 0 B) Monomial; 13 C) Monomial; 1 D) Monomial; 0
Answer: C 99) 14a7
A) Binomial; 7 B) Monomial; 14 C) None of these; 14 D) Monomial; 7 Answer: D
100) 16y7 + 5
A) Binomial; 0 B) Binomial; 7 C) Binomial; 8 D) Monomial; 16
Answer: B
101) -5z - 8
A) Binomial; 0 B) Binomial; 1 C) Monomial; -5 D) Binomial; 2
Answer: B 102) -6s3 + 7s + 3
A) Binomial; 4 B) None of these; 5 C) Trinomial; 4 D) Trinomial; 3
Answer: D
103) -11y5 + 7y4 - 7
A) None of these; 5 B) Trinomial; 10 C) Trinomial; 5 D) Binomial; 5
Answer: C
104) -18c5 + 6c4 - 3c3
A) Trinomial; 5 B) None of these; 5 C) Trinomial; 12 D) Binomial; 12
Answer: A
105) 19z5 + 6z4 + 2z3 + 12
A) Trinomial; 5 B) Trinomial; 12 C) None of these; 5 D) Binomial; 13
Answer: C 106) 14x3 - 5w2 + 5w - 2y4 + 3
A) Binomial; 11 B) None of these; 10 C) Trinomial; 4 D) None of these; 4
Answer: D
Combine terms. 107) -8y - 6x - 2x
A) -8y - 8x B) -8y + 4x C) -8y - 4x D) -16xy
Answer: A 108) -2y4 - 2y4
A) -4y8 B) 4y8 C) -4y4 D) 4y4 Answer: C
18
Answer: D
19 109) -8x9 + 7x9 + 9x9 A) -504x27 B) -504x9 C) 8x9 D) 8x27 Answer: C 110) -9m3 - 10m + 2m3 - 9 A) -17m2 - 9 B) 180m5 - 9 C) -7m3 - 10m - 9 D) -26m5 Answer: C 111) z3 + 12z4 + 5z2 + z4 - 9z3 A) 13z8 - 10z6 + 5z2 B) 12z4 - z3 + 5z2 C) 13z4 - 8z3 + 5z2 D) -13z4 + 10z35z2 Answer: C Add or subtract as indicated 112) (9a5 - 3a3) + (7a5 - 7a3) A) 16a10 - 10a6 B) 6a16 C) 16a5 - 10a3 D) 6a8 Answer: C 113) (4n5 + 6n + 5n2) + (-9n2 + 3n5 + 3n) A) 7n5 - 4n2 + 9n B) 9n5 - 5n2 + 8n C) 12n8 D) 7n - 4n5 + 9n2 Answer: A 114) (2 + 5x7 + 9x9 + 4x8) + (2x8 + 3x7 + 6 + 9x9) A) 4x9 + 4x8 + 15x7 + 13 B) 18x18 + 6x16 + 8x14 + 8 C) 32x48 + 8 D) 18x9 + 6x8 + 8x7 + 8 Answer: D 115) (-8x7 + 2x9 - 2 - 9x8) - (-3 + 7x8 + 4x9 + 4x7) A) -2x9 - 2x8 - 4x7 - 5 B) 6x9 - 2x8 - 4x7
D)
+ 1 C) 6x9 - 2x8 - 4x7 - 5
-2x9 - 16x8 - 12x7 + 1
116)
B)
D)
B)
D)
(-2r4 + 9r3 - 3r) - (8r4 - 9r3 + 6r2 - 2r) A) -10r4 + 18r3 - 6r2 - r
-6r4 - 6r2 + r C) 10r4 - 18r3 + 6r2 + r
6r4 + 6r2 - r Answer: A 117) (-6x3 + 9x2 + 4) - (-5x3 + 2x - 5) A) -x3 + 9x2 + 2x - 1
-x6 + 9x4 - 2x2 + 9 C) -x3 + 9x2 - 2x + 9
-11x3 + 9x2 + 2x - 1 Answer: C
20 118) (-6 + 4x3 + 5x5 + 7x4) + (2x4 + 8x3 + 5 + 5x5) A) 10x5 + 9x4 + 12x3 - 1 B) -4x5 - 4x4 + 10x3 + 12 C) 31x24 - 1 D) 10x10 + 9x8 + 12x6 - 1 Answer: A 119) (4x5 + 3x7 - 3 - 5x6) - (4 + 8x6 + 9x7 + 8x5) A) -6x7 - 13x6 - 4x5 - 7 B) -6x7 + 3x6 + 12x5 + 1 C) 12x7 + 3x6 + 12x5 + 1 D) 12x7 + 3x6 + 12x5 - 7 Answer: A 120) (11x9 + 3x7 - 3x3 + 4) - (3x9 - 6x4 + 10x3 - 3) A) -8x9 + 3x7 + 6x4 - 13x3 + 7 B) -8x9 + 3x7 - 6x4 - 13x3 + 7 C) 8x9 + 3x7 + 6x4 - 13x3 + 7 D) 8x9 + 3x7 - 6x4 - 13x3 + 7 Answer: C 121) Subtract -8y - 7 -5y + 6 A) -13y - 1 B) 3y - 13 C) -3y - 13 D) 13y - 1 Answer: C 122) Add. 3m - 11 8m + 10 A) -5m - 21 B) -11m - 1 C) 5m - 21 D) 11m - 1 Answer: D 123) Add 7x3 - 2x - 8 -3x3 + 4x - 12 A) -33x3 - 2x + 20 B) 4x3 + 2x - 20 C) 10x - 6x + 4 D) -34x + 6x4 Answer: B 124) Subtract. 5z2 + 12z - 10 -11z2 + 7z - 2 A) 6z2 - 19z + 12 B) -16z2 - 5z + 8 C) -6z2 + 19z - 12 D) 16z2 + 5z8 Answer: D
125) Subtract. 10x3 + 3x2 - 3 -12x3 - 9x2 - 9x
-33x3 + 6x2 + 9x + 3
126) Add. -4z4 + 6z3 -z3 + 12z
Tell whether the statement is true always, sometimes, or never 127) A binomial is a polynomial.
128) A trinomial is a polynomial. A) Always B) Never
A
129) A polynomial is a trinomial. A) Always B) Sometimes C) Never Answer: B
130) A monomial has no coefficient A) Always B) Never C) Sometimes Answer: B
131) A trinomial is a monomial. A) Always B) Never C) Sometimes
Answer: B
132) A polynomial of degree 6 has 6 terms A) Never B) Sometimes C) Always
Answer: B
For the polynomial function, find the requested value.
133) f(x) = -6x + 9; f(3) A) -36 B) 3
Answer: C
134) f(x) = 5x2 - 9x - 2; f(3)
-14 B) 6
-9 D) -27
21
B) -34x3 - 12x2 - 9x + 3
D) 22x3 + 12x2 + 9x
3
A)
C) -2x3 - 6x2 - 9x - 3
-
Answer: D
A) -3z4 + 6z3 - 12z B) -4z4 + 5z3 + 12z C) -4z4 + 7z3 - 12z D) -4z4 + 7z3 + 12z
Answer: B
B)
C)
A) Sometimes
Always
Never Answer: B
C) Sometimes Answer:
C)
C)
A)
12 D) 16
22 Answer: D
Solve the problem.
142) The polynomial 0.0051x3 - 0.0045x2 + 0.144x + 1.95 gives the approximate total earnings of a company, in millions of dollars, where x = 0 corresponds to 1996, x = 1 corresponds to 1997, and so on. This model is valid for the years from 1996 to 2000. Determine the earnings for 2000. Round your answer to the nearest hundredth million.
A) $2.78 million B) $2.48 million C) $2.92 million D) $3.2 million
Answer: A
143) The polynomial 0.0055x4 - 0.0032x3 + 0.0046x2 + 0.18x + 1.26 gives the predicted sales volume of a company, in millions of items, where x is the number of years from now. Determine the predicted sales 11 years from now. Round your answer to the nearest hundredth million A) 71.11 million B) 80.06 million C) 107.88 million D) 135.75 million
Answer: B
144) A(x) = -0.015x3 + 1.05x gives the alcohol level in an average person's bloodstream x hours after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 7 hours?
A) Yes B) No
Answer: A
23 135)
A)
B)
C)
D)
Answer:
A)
B)
C)
D)
Answer:
137)
A) 16 B) 6 C) 46 D) 4 Answer:
138) f(x)
A) -42 B)
C) -44 D)
68 Answer:
139)
A) 8 B)
C) 12 D)
Answer:
140)
A)
4 B)
C)
D)
Answer:
141) f(x)
f(4) A) 42 B) 72 C)
D) 15 Answer:
f(x) = -3x2 - 4x - 10; f(-3)
-25
11
-35
-29
A 136) f(x) = 5x3 - 5x2 - 42; f(2)
-32
-12
-34
-22
D
f(x) = -4x3 - 5x2 + 4; f(-2)
A
= 4x3 + 6x2 - x - 26; f(-2)
-32
-
B
f(x) = 4x5 - 6x4 - 2x3 - x2; f(2)
7
41
C
f(x) = 2x5 + 5x4 + 2x3 - x2; f(-2)
-
-8
25
-9
A
= 9x + 6;
30
A
145) The polynomial function L(p) = p3 - 5p2 + 20 gives the rate of gas leakage from a tank as pressure increases p units from its initial setting. Will an increase of 3 units result in a lower rate of leakage compared to the initial setting?
A) No
Answer: B
For the given pair of functions, find the requested function 146)
B) Yes
24
f(x)
g(x)
A) 13x - 6 B) -3x2 + 6 C) -4x + 10 D) -3x + 6 Answer: D 147) f(x)
4x
4, g(x)
g)(x) A) -4x - 5 B) 12x - 13 C) 12x + 13 D) -4x2 + 13 Answer: B 148) f(x)
x2 + 3x - 4, g(x) = -7x2 + 6x - 4; (f + g)(x) A) -8x2 + 9x + 8 B) -7x2 + 9x + 8 C) -6x2 + 9x - 8 D) -6x2 - 9x - 8 Answer: C 149) f(x) = x2 + 4x - 2, g(x) = -9x2 + 8x - 10; (f - g)(x) A) 10x2 - 12x + 18 B) -8x2 + 12x - 8 C) -9x2 - 12x + 8 D) 10x2 - 4x + 8 Answer: D 150) f(x) = 5x - 2, g(x) = -9x2 - 10x + 7; (f + g)(x) A) -10x2 - 5x - 5 B) -9x2 - 5x + 5 C) 9x2 - 4x - 9 D) -9x2 + 5x + 5 Answer: B 151) f(x) = 3x - 4, g(x) = -8x2 - 12x + 6; (f - g)(x) A) 8x2 + 15x - 10 B) 8x2 - 9x - 10 C) -8x2 + 15x + 10 D) -8x2 - 9x + 2 Answer: A Provide an appropriate response. 152) Let f(x) = x2 - 2 and g(x) = 4x + 9. Find (f - g)(4). A) -13 B) -10 C) -11 D) -6 Answer: C 153) Let f(x) = x2 - 3 and g(x) = 2x + 8. Find (f + g)( 1 ). 2 A) 13 2 Answer: D B) 6 C) 29 4 D) 25 4
the composition of
= 5x - 2,
= -8x + 8; (f + g)(x)
=
-
= -8x + 9; (f -
=
Evaluate
functions.
154) Let f(x) = x2 + 4 and g(x) = 2x + 7. Find (g ∘ f)(5)
65
51
25
A)
C)
D)
B) 36
293 Answer: A
155) Let f(x) = 6x + 3 and g(x) = x + 8. Find (f ∘ g)(2). A) 150 B) 25
63 Answer: D
Find (f ∘g)(x) for the given functions f(x) and g(x). 156) f(x) = 7x + 9 and g(x) = 5x - 1
f(x) = x + 5 and g(x) = 8x - 4
161) f(x) = 9x + 6 and g(x) = x2 - 5 A) 9x2 - 39
x2 - 9x11
Answer: A
Answer the question
x2 + 9x + 1
162) The function f(x) = 60x computes the number of minutes in x hours The function g(x) = 24x computes the number of hours in x days What is (f ∘ g)(x) and what does it compute?
A) (f ∘ g)(x) = 1440x; it computes the number of days in x minutes.
B) (f ∘ g)(x) = 84x; it computes the number of minutes plus the number of days in x days.
C) (f ∘ g)(x) = 1440x2; it computes the number of minutes in x days. D) (f ∘ g)(x) = 1440x; it computes the number of minutes in x days.
Answer: D
26
C)
D)
23
A) 35x
B) 35x + 2 C) 35x + 16 D) 35x + 44
A) 36x
B) 12x C) 14 D) 36x
35
158)
A) 9x
B) 8x + 36 C) 8x + 1 D) 7x + 9
159) f(x)
g(x)
A) 30x +
B) -30x + 44 C) -30x D) -30x + 17
160) f(x)
g(x)
A) 12x
B) 2x + 3 C) 8x - 15 D) 8x - 18
+ 8
Answer: B 157) f(x) = 6x + 7 and g(x) = 6x - 7
+ 35
-
Answer: D
+ 1
Answer: C
= 5x + 7 and
= -6x + 2
17
Answer: D
= 2x - 3 and
= 4x - 6
- 9
Answer: C
C)
D)
B)
81x2 + 18x - 6
163) A balloon in the shape of a sphere is deflating. Given that t represents the time, in minutes, since it began losing air, the radius of the balloon (in cm) is r(t) = 20 - t Let the equation V(r) = 4 πr3 represent the volume of a 3 sphere of radius r. Find and interpret (V ∘ r)(t).
A) (V ∘ r)(t) = 4 π(20 - t)3; this is the volume of the balloon (in cm3) as a function of time (in minutes). 3
B) (V ∘ r)(t) = 4 π(t - 20)3; this is the volume of the balloon (in cm3) as a function of time (in minutes). 3
C) (V ∘ r)(t) = 4 π(20 - t)3; this is the volume of the air lost by the balloon (in cm3) as a function of time (in 3 minutes).
D) (V ∘ r)(t) = 204 π(20 - t)3; this is the volume of the air lost by the balloon (in cm3) as a function of time 3 (in minutes).
Answer: A
Give the domain and range of the function.
164) f(x) = -3x - 9
A) Domain: (-∞ , ∞); range: (-∞ , -9)
B) Domain: (-∞ , ∞); range: (-∞ , ∞)
D) Domain: (0, ∞); range: (-∞ , 0) Answer: B
C) Domain: (-3, ∞); range: (-∞ , 9)
165) f(x) = 9x
A) Domain: (-∞ , ∞); range: (-∞ , ∞)
C) Domain: (-∞ , 9); range: (-9, ∞)
∞) Answer: A
166) f(x) = 3x2 - 3
A) Domain: (-∞ , ∞); range: (-3, ∞)
B) Domain: (-9, 9); range: (-∞ , ∞)
D) Domain: (-∞ , -9); range: (-∞ ,
B) Domain: (-∞ , 3); range: (-∞ ,
∞)
C) Domain: (-3, ∞); range: (-∞ , ∞)
D) Domain: (-∞ , ∞); range: (-∞ , 3)
Answer: A
167) f(x) = -4x2 - 9
A) Domain: (-∞ , ∞); range: (-∞ , ∞)
C) Domain: (-4, ∞); range: (9, ∞)
Answer: D
168) f(x) = x3 + 7
A) Domain: (0, ∞); range: (-∞ , ∞)
C) Domain: (-∞ , ∞); range: (-∞ , 0)
Answer: D
169) f(x) = -x3 + 8
B) Domain: (-∞ , ∞); range: (-9, ∞)
D) Domain: (-∞ , ∞); range: (-∞ , -9)
B) Domain: (-7, ∞); range: (-∞ , 7)
D) Domain: (-∞ , ∞); range: (-∞ , ∞)
27
A) Domain: (-8, ∞); range: (-∞ , ∞)
B) Domain: (-∞ , ∞); range: (-∞ , 8)
D) Domain: (-∞ , ∞); range: (-∞ , ∞) Answer: D
C) Domain: (-∞ , ∞); range: (0, ∞)
28
A) Domain: (-∞ , ∞); range: (-∞ , 0)
C) Domain: -∞ , 1 ; range: (-∞ , 0)
B) Domain: (-∞ , ∞); range: (-∞ , ∞)
D) Domain: (-∞ , ∞); range: (0, ∞)
A) Domain: (-∞ , ∞); range: (-∞ , ∞)
C) Domain:1 , ∞ ; range: (-∞ , 0)
B) Domain: (-∞ , ∞); range: (0, ∞)
D) Domain: (-∞ , ∞); range: (-∞ , 0)
29
170) f(x) = 1 x2 8
8
171)
1
9
Answer: D
f(x) = -
x2
9
D Graph the function 172) f(x) = x2 - 2 y 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 A) B) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5
Answer:
30 C) D) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 Answer: B 173) g(x) = x2 + 2x - 2 y 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 A) B) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5
31 C) D) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 Answer: D 174) r(x) = 3 y 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 A) B) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5
32 C) D) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 Answer: A 175) r(x) = x3 - 2x + 1 y 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 A) B) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5
33 C) D) y y 5 5 4 4 3 3 2 2 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4 -5 Answer: C Find the product. 176) (4m4)(2m2) A) -8m6 B) 8m C) 8m6 D) -8m Answer: C 177) (-3m4)(3m4) A) 9m6 B) 9m C) -9m D) -9m8 Answer: D 178) (-2x4y4)(3x3y2) A) 6xy7 B) 6x6y7 C) 6xy6 D) 6x7y6 Answer: D 179) 2x5(-5x + 6) A) -10x5 + 12 B) -10x6 + 12x5 C) 2x6 D) 10x6 - 12x5 Answer: B 180) 3x3(-10x7 + 10x2) A) -30x21 + 30x6 B) -30x10 - 30x5 C) -30x10 + 10x2 D) -30x10 + 30x5 Answer: D 181) -11ax2(
11ax4
4) A) 121a2x6
B) 121ax8 - 77ax6 - 44ax2 C) -121a2x8 +
+
D) -121a2x6 + 77ax5 + 44ax2 Answer: A 182) -4ax4(-7ax3 + 7x2 + 6a) A) 28a2x12 - 28ax8 - 24a2x4 B) 28a2x7 + 28ax6 + 24a2x4 C) 28ax7 - 28ax6 - 24ax4 D) 28a2x7 - 28ax6 - 24a2x4 Answer: D
-
+ 7x3 +
- 77ax5 - 44ax2
77ax6
44ax2
183) -7a3x4(-12a5x9 - 3x5 - 9a)
84a15x36 - 21a3x20 - 63a3x4
- 21a3x9 - 63a4x4 C) 84a8x13 - 3x5 - 9a
+ 21a3x9 + 63a4x4
34
B) -84a8x13
D) 84a8x13
Answer: D 184)
5x2(
4x6) A) 25x9 + 25x8 B) 45x9 - 20x8 C) 25x2 D) 45x9 + 4x6 Answer: B 185)
A) 12m7z6 B) 12mz6 C) 12m7z D) 12mz7 Answer: A 186) (3x - 11)(x + 9) A) 3x2 + 15x - 99 B) x2 + 16x + 15 C) 3x2 + 16x - 99 D) x2 - 99x + 16 Answer: C 187) (x + 10)(4x - 8) A) x2 + 32x + 32 B) 4x2 + 32x - 80 C) 4x2 - 80x + 32 D) 4x2 + 31x - 80 Answer: B 188) (x + 2)(-5x - 3) A) -5x2 - 13x - 13 B) -5x2 - 15x - 6 C) -5x2 - 13x - 6 D) -5x2 - 6x - 13 Answer: C 189) (x + 10y)(x + 3y) A) x2 + 13xy + 13y2 B) x2 + 13xy + 30y2 C) x2 + 10xy + 30y2 D) x + 13xy + 30y Answer: B 190) (-7a - 9b)(-2a - 3b) A) 14a2 - 39ab + 27b2 B) 14a2 + 39ab + 27b2 C) 14a2 + 3ab + 27b2 D) 14a2 + 27b2 Answer: B 191) (11 + x)(4x + 1) A) 4x2 + 11x + 45 B) 4x2 + 44x + 11 C) x2 + 45x + 45 D) 4x2 + 45x + 11 Answer: D 192) (x + 1)(-3x - 2) A) -3x2 - 7x - 2 B) -3x2 - 5x - 5 C) -3x2 - 5x - 2 D) -3x2 - 2x - 5 Answer: C 193) (9p - 1)(81p2 + 9p + 1) A) 81p3 - 1 B) 729p3 + 1 C) 729p3 - 1 D) 729p3 + 90p21 Answer: C
A)
-
-9x7 +
(4m4z4)(3m3z2)
194) (3y - 4)(9y2 + 12y + 16)
A) 27y3 + 48y2 - 64
Answer: C
195) (-2x + 4y)(3x + 11y + 1)
27y3 + 64
27y3 - 64
9y3 + 64
A) -6x2 - 10xy - 2x + 44y2 + 4y B) -6x2 - 10xy - 10y2
C) -6x2 - 22xy - 2x + 44y2 D) -6x2 + 12xy - 2x + 44y2 + 4y
Answer: A
196) (-5x2 + 9y)(-4x2 - 3y + z)
A) 20x4 - 21x2y - 5x2z - 27y2 + 9yz B) 20x2 - 21xy - 5x2z - 27y2 + 9z
C) 20x4 - 21x2y2 - 27y2 D) 20x4 - 21x2y - 27y4 - 5x2yz
Answer: A
197) (2x2 + 2x - 3)(x2 - 4x - 1) A) 2x4 - 6x3 - 13x2 + 10x + 3
- 8x3 - 13x2 + 10x + 3
Answer: A
198) (3y2 - 2y - 1)(y2 + 4y - 3) A) 3y4 + 12y3 - 17y2 + 2y + 3
2x4 - 6x3 - 10x2 + 10x + 3
3y4 + 10y3 - 18y2 + 2y + 3 C) 3y4 + 10y3 - 17y2 + 2y + 3
Answer: B
199) (4r - 2)(5r3 + 2r2 + 3r - 2) A) 20r4 -
Answer: A 200) (2x3- x2 + 3x - 1)(2x + 3) A) 3x4 + 8x3 + 6x2 + 9x - 5
-
4x4 + 4x3 + 3x2 + 7x - 3 C) 5x4 - 4x3 + 2x2 - 7x + 3
Answer: B 201) 4x(4x - 1)(5x + 8) A) 80x3 + 108x2 - 32x B) 78x2 + 109x - 32
76x3 + 110x230x Answer: A
(a - 7)(a + 7) A) a2 - 14
35
B)
D)
C)
B)
2x4 - 8x3 - 10x2 + 10x + 3 C) 2x4
D)
B)
D)
3y4 + 12y3 - 18y2 + 2y + 3
4 B) 20r4
C)
4 D) 20r4
B)
D)
2r3 + 8r2 - 14r +
+ 4r3 + 8r2 - 14r + 4
20r4 - 2r3 + 8r2 - 8r +
- 2r3 + 6r2
14r + 4
4x3 + 4x2 + 3x + 7
C)
D)
B)
C)
D)
20x3 + 27x2 - 8x
202)
a2 - 49
a2 + 14a - 49
a2 - 14a - 49 Answer: B
13c2
64a2 + 208ac - 169c2
64a2 - 208ac - 169c2 Answer: C
64a2 - 169c2
4m2 - 121w2
36 203) (m + 13)(m - 13) A) m2 - 26m - 169 B) m2 - 169 C) m2 - 26 D) m2 - 26m + 169 Answer: B 204) (n - 10)(n + 10) A) n2 - 20n + 100 B) n2 - 20n - 100 C) n2 - 20 D) n2 - 100 Answer: D 205) (11p + 5)(11p5) A) 121p2 - 25 B) 121p2 + 110p - 25 C) p2 - 25 D) 121p2 - 110p25 Answer: A 206) (2r - 3)(2r + 3) A) 4r2 - 12r - 9 B) 2r2 - 9 C) 4 + 12r - 9r2 D) 4r2 - 9 Answer: D 207) (p + 9q)(p - 9q) A) p2 - 18pq - 81q2 B) p2 - 18q2 C) p2 + 18pq - 81q2 D) p2 - 81q2 Answer: D 208) (9y + x)(9y - x) A) 81y2 + 18xy - x2 B) 81y2 - 18xy - x2 C) 18y2 - x2 D) 81y2 - x2 Answer: D 209) (8a + 13c)(8a - 13c) A) 8a2 -
B)
D)
210)
A)
B)
C)
D)
211)
A)
B)
C)
D)
212)
A)
B)
C)
D)
213)
A)
B)
C) w +
D)
Answer:
C)
(2m - 11w)(2m + 11w)
2m2 - 11w2
4m2 + 44mw - 121w2
4m2 - 44mw - 121w2 Answer: C
(n + 8)2
n + 64
n2 + 64
64n2 + 16n + 64
n2 + 16n + 64 Answer: D
(p + 3)2
p + 9
p2 + 9
p2 + 6p + 9
9p2 + 6p + 9 Answer: C
(w - 7)2
49w2 - 14w + 49
w2 + 49
49
w2 - 14w + 49
D
37 214) (r - 8)2 A) r + 64 B) r2 - 16r + 64 C) r2 + 64 D) 64r2 - 16r + 64 Answer: B 215) (3m + 8)2 A) 3m2 + 48m + 64 B) 3m2 + 64 C) 9m2 + 48m + 64 D) 9m2 + 64 Answer: C 216) (3a - 8)2 A) 3a2 - 48a + 64 B) 9a2 + 64 C) 9a2 - 48a + 64 D) 3a2 + 64 Answer: C 217) (-3x - 5)2 A) -3x2 + 30x + 25 B) -3x2 + 25 C) 9x2 + 25 D) 9x2 + 30x + 25 Answer: D 218) (8x + 9y)2 A) 64x2 + 144xy + 81y2 B) 8x2 + 144xy + 81y2 C) 8x2 + 81y2 D) 64x2 + 81y2 Answer: A 219) (4x - 5y)2 A) 4x2 + 25y2 B) 16x2 - 40xy + 25y2 C) 16x2 + 25y2 D) 4x2 - 40xy + 25y2 Answer: B 220) (3.1x - 8y)(3.2x + 7y) A) 9.92x2 - 56y2 B) 9.92x2 - 3.9xy - 56y2 C) 9.92x - 3.9xy - 56y D) 9.92x2 - 47 3xy - 56y2 Answer: B 221) (0.6x - 1.1y)2 A) 0.36x2 - 1.21y2 B) 0.36x2 + 1.32xy + 1.21y2 C) 0.36x2 + 1.21y2 D) 0.36x2 - 1.32xy + 1.21y2 Answer: D 222) 4x1 y (x + 5y) 2 A) 4x239 xy5 y2 B) 4x27 xy5 y2 C) 4x2 + 39 xy + 1 y2 D) 4x2 + 39 xy5 y2 2 2 2 2 Answer: D 2 2 2 2
225) [(4x + 1) + 8y]2
A) 16x2 + 8x + 64xy + 16y + 64y2 B) 16x2 + 4x + 1 + 32xy + 8y + 64y2
C) 16x2 + 64xy + 64y2
Answer: D
226) [(2x - 2) + 7y]2
A) 4x2 - 8x + 28xy - 28y + 49y2
C) 4x2 - 8x + 4 + 14xy + 14y + 49y2
Answer: D
227) [(3x - y) + 4z][(3x - y) - 4z]
A) 9x2 + y2 + 24xz + 8yz - 16z2
C) 9x2 - 6xy + y2 + 24xz + 8yz - 16z2
Answer: B
228) (x + 2y)3
A) x3 + 6x2y + 12xy2 + 8y3
D) 16x2 + 8x + 1 + 64xy + 16y + 64y2
B) 4x2 - 4x + 4 + 14xy + 14y + 49y2
D) 4x2 - 8x + 4 + 28xy - 28y + 49y2
B) 9x2 - 6xy + y2 - 16z2
D) 9x2 + y2 - 16z2
B) x3 + 2x2y + 4xy + 4xy2 + 8y2 + 8y3
D) 3(x + 2y) Answer: A
C) x3 + 8y3
229) (2x + 5)3
A) 4x2 + 20x + 25
C) 4x6 + 10x3 + 15,625
Answer: B
230) (5x + 2)4
A) 625x3 + 1000x2 + 600x + 160
C) (25x2 + 10x + 4)
Answer: D
4
B) 8x3 + 60x2 + 150x + 125
D) 8x3 + 60x2 + 60x + 125
B) 1250x4 + 2000x3 + 600x2 + 320x + 16
D) 625x4 + 1000x3 + 600x2 + 160x + 16
38 223) 3t8 7 3t + 8 7 A) 9t248 t64 B) 9t264 C) 9t2 + 48 t D) 9t2 + 64 7 49 49 7 49 Answer: B 224) q7 r 2 10 A) q27 qr + 49 r2 B) q2 + 49 r2 C) q27 qr49 r2 D) q249 r2 5 Answer:
100 100 10 100 100
A
Express the area of the figure as a polynomial in descending powers of the variable x.
For the pair of functions, find the product (fg)(x).
39
231) 3x - 3 x + 7 A) 3x2 + 24x - 14 B) -3x2 + 17x + 21 C) 3x2 + 18x - 21 D) 2x2 - 24x + 21 Answer: C 232) 5x - 3 2x + 3 A) 10x2 - 10x - 9 B) 10x2 + 9x - 9 C) -10x2 + 9x + 9 D) 5x2 + 15x - 3 Answer: B 233) x + 4 x + 4 A) x2 + 8x + 16 B) x2 + 4x + 4 C) x2 - 8x + 16 D) x2 + 4x + 16 Answer: A 234) 5x - 3 4x + 8 A) 10x2 + 34x - 48 B) 22x2 + 30x - 24 C) 9x + 5 D) 20x2 + 28x - 24 Answer: D x2 + 5x - 1 235) 4x + 2 A) 2x3 - 11x2 + 3x + 1 B) 2x3 - 9x2 - 7x - 1 C) 2x3 + 9x2 + 7x - 1 D) 2x3 + 11x2 + 3x1 Answer: D
236) f(x) = 4x, g(x) = 8x - 5 A) -32x2 - 20x B) 32x2 - 20x C) 12x2 - 5x D) 32x - 20 Answer: B
237) f(x) = 4x + 4, g(x) = 2x - 7 A) 8x2 - 20x - 28
- 36x + 28 Answer: A 238) f(x) = 4x + 4, g(x) = -4x - 7
Answer: C 239) f(x) = 4x + 3, g(x) = x2 + 6x - 7
A) x3 - 27x2 - 22x - 24
C) x2 - 10x + 4
Answer: D
240) f(x) = 5x + 3, g(x) = -x2 + 5x + 8
A) -5x3 - 23x2 + 55x - 24
C) 5x3 + 22x2 - 55x - 24
Answer: D
Find the requested value.
241) If f(x) = x2 + 4x + 8 and g(x) = 9x - 1, find (fg)(x).
A) 9x3 + 35x2 + 68x - 8
C) 81x2 + 18x + 5
Answer: A
242) If f(x) = x2 + 8x + 5 and g(x) = 7x - 2, find (fg)(-4).
A) -1398
Answer: D
B) 382
243) If f(x) = 5x + 7 and g(x) = 8x2 - 6x + 8, find (fg)(x).
A) 40x3 + 26x2 - 2x
C) 40x3 - 26x2 - 2x + 56
Answer: D
244) If f(x) = 8x + 3 and g(x) = 6x2 - 7x + 2, find (fg)(2).
A) 228 B) 99
Answer: A
5x3 + 29x2 + 10x - 20
4x3 + 27x2 - 10x - 21
-10x2 + 22x2 - 55x + 24
-5x3 + 22x2 + 55x + 24
B) 9x3 + 35x2 + 4x - 1
D) 9x3 - 35x2 - 68x - 8
C) -7
D) 330
B) 40x2 - 30x + 47
D) 40x3 + 26x2 - 2x + 56
C) 532
D) 222
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.
245) Explain how to find the product of two monomials by using the following example:
8m2z5q4 10m5zq3
Answer: Answers will vary, but should explain that coefficients are multiplied and exponents are added The exponent on the second z factor is 1.
40
B)
C)
D)
B)
C)
D)
30
2x2 - 26x - 56
6x2 + 19x - 28
8x2
A) -14x2 + 44x - 28
16x2 + 44x - 28
-16x2 - 44x - 28
-17x2 - 46x -
B)
D)
B)
D)
246) Explain how to find the product of two polynomials by using the following example: (-4m - 9)(-7m2 - 6m - 5)
Answer: Answers will vary, but should should demonstrate that each term in the first polynomial must be multiplied by each term of the second, and that similar terms must be combined
247) Give an example of two polynomials which can be multiplied by the FOIL method. Use your example to explain the method.
Answer: Answers will vary, but should include two binomials and demonstrate the use of the technique.
248) Give an example of two binomials whose product is a binomial.
Answer: Answers will vary, but should be the sum and difference of two terms.
249) Explain how you can use the special product (a + b)(a - b) to find the product of 94 86.
Answer: Answers will vary, but should equate 94 86 with (90 + 4)(90 - 4), which equals 902 - 42
250) Are the two expressions equivalent? Give numerical values for x and y to back up your answer. (x + y)5 ; x5 + y5
Answer: The two expressions are not equivalent Examples will vary, but any nonzero values for x and y should demonstrate this.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Divide.
41
251) -4x6+ 8x4 -2x2 A) -4x6 - 4x2 B) 2x4 + 8x4 C) -2x8 D) 2x4 - 4x2 Answer: D 252) 20x7- 8x3 -4x7 A) -5 + 2 x4 Answer: A 253) 30x6+ 48x5+ 36x4 6x5 B) -5 - 8x3 C) 20x7 + 2 x4 D) -5 + 2x4 A) 11x + 8 B) 5x + 8 + 6 x C) 5x + 8 D) 5x + 48x5 + 6 x Answer: B 254) 42x5- 49x4+ 21x3 7x4 A) 9x - 7 B) 6x - 49x4 + 3 x C) 6x - 7 D) 6x - 7 + 3 x
42 Answer: D
43 255) -40x8+ 64x6- 32x4 -8x6 A) 5x - 8 + 4 x2 B) 5x - 8 + 4 x C) 5x2 - 8 + 4 x D) 5x2 - 8 + 4 x2 Answer: D 256) 16st3- 5t4+ 64st2 4st2 A) 4t5t2 + 16 B) 4st5t2 + 16 C) 4t - st2 + 16 D) 4tt2 + 16 4s 4s s Answer: A 257) x2+ 17x+ 72 x + 9 A) x2 + 8 B) x - 63 C) x3 - 63 D) x + 8 Answer: D 258) x2+ 5x- 14 x + 7 A) x2 + 6x - 7 B) x + 2 C) x - 2 D) x2 - 2 Answer: C 259) 4m2+ 29m- 24 m + 8 A) 4m + 3 B) 4m - 3 C) 4m - 3 + 2 m - 3 D) m - 3 Answer: B 260) y2+ 14y+ 49 y + 7 A) y2 + 7 B) y + 7 y + 7 C) y + 7 D) y - 7 Answer: C 261) x2+ 11x+ 17 x + 8 A) x+ 3 x + 8 Answer: B 262) x211 x+ 24 x - 8 B) x + 37 x + 8
44 C) x + 4 D) x + 3 + 7 x + 8 A) x + 8 B) x + 3 C) x - 3 D) 3 - x Answer: C
45 263) -15x3- 32x2+ 4x+ 16 5x + 4 A) -3x2 - 4x + 4 B) x2 - 4x + 4 C) -3x2 + 4 D) x2 + 4x - 4 Answer: A 264) 9y4+ 6y3+ 2y- 1 3y2 + 1 A) 3y2 - 2y + 1 B) 3y2 + 2y C) 3y2 - 1 D) 3y2 + 2y1 Answer: D 265) 7m3+ 28m2- 28m+ 35 7m2 - 7m + 7 A) m - 5 B) m2 + 5 C) m2 - 5 D) m + 5 Answer: D 266) 2r3 - 4r2 - 8r32 2r2 + 4r + 8 A) r - 4 B) r + 4 C) r2 - 4 D) r2 + 4 Answer: A 267) (5z4 - 2z3 + 6z2 + 6z + 6) ÷ (z2 - z + 2) A) 5z2 + 3z - 1 B) 5z2 - 3z + 1 + z- 8 z2 - z + 2 C) 5z2 + 3z - 1 + z- 8 z2 - z + 2 D) 5z2 + 3z - 1 + -z+ 8 z2 - z + 2 Answer: D 268) 2q273 q - 4 ÷ (9q + 4) 9 A) q2 - 73q - 1 B) -7q2109 q - 4 C) 2 q - 1 D) 2 q + 1 Answer: C 9 9 9 269) 9r2 + 14r + 5 ÷ (5r + 5) A) 9 r + 1 B) r2 + 70r + 1 C) 4r2 + 19r + 5 D) 9 r - 1 5 5 Answer: A 270) (3q2 - 8q + 5) ÷ (5q - 5) A) q2 + 40q + 1 B) 3 q + 1 C) -2q2 - 13q + 5 D) 3 q - 1 5 5
