Test Bank for College Algebra Essentials, 5th Edition

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Ch. 0Chapter P: Prerequisites: Fundamental Concepts of Algebra0.1Algebraic Expressions, Mathematical Models, and Real Numbers1Evaluate Algebraic ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the algebraic expression for the given value or values of the variable(s).1) 4x+8;x=4A) 24B) 32C) 12D) 82)-4x-6;x=-3A) 6B)-18C) 18D)-63) 6(x+9)+21;x=-19A)-39B) 39C) 195D)-1534) 3x2+7y;x=4 and y=9A) 111B) 207C) 621D) 2715) (x+3y)2;x=3 and y=2A) 81B) 9C) 18D) 366) 5+6(x-7)3;x=9A) 53B) 17C) 88D)-437) x2-5(x-y);x=8 and y=2A) 34B) 22C) 26D)-948) 9(x-1)2x+4 ;x=7A) 3B) 4C) 6D) 529)y-2x4x+xy ;x=-4 and y=5A)-1336B)112C)-34D)-5362Use Mathematical ModelsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve.1) The formula C=59 (F-32) expresses the relationship between Fahrenheit temperature, F, and Celsiustemperature, C. Use the formula to convert 41°F to its equivalent temperature on the Celsius scale.A) 5°CB) 1°CC) 41°CD) 16°CPage 1

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2) A stone is dropped from a tower that is 740 feet high. The formula h=740-16t2 describes the stone'sheight above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 1 secondsafter it is released?A) 724 ftB) 734 ftC) 699 ftD) 749 ft3) If a rock falls from a height of 90 meters above the ground, the height H (in meters) after x seconds can beapproximated using the formula H=90-4.9x2. What is the height of the rock after 4 seconds?A) 11.6 mB) 1361.6 mC)-294.16 mD) 70.4 m4) As the relative humidity increases, the temperature seems higher than it is. The formula T=0.101x+55.05approximates the apparent temperature for an actual temperature of 60°F, where x is the relativehumidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 70%?A) 62°FB) 389°FC) 125°FD) 55°F5) The winning times (in seconds) in a speed-skating event for men can be represented by the formulaT=46.85-0.094x, where x represents the year, with x=0 corresponding to 1920. (For example in 1992, xwould be 1992-1920=72.) According to the formula, what was the winning time in 1964? Round to thenearest hundredth.A) 42.71 secB) 2057.26 secC) 43.65 secD) 44.59 sec6) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United Statesin year x, where x represents the number of years since 1990, is given by the formula y=1.56x+3.56. Thatis, x=0 represents 1990, x=1 represents 1991, and so on. According to the formula, how many items soldin 2000?A) 19.16 millionsB) 3.56 millionsC) 51.20 millionsD) 20.72 millions3Find the Intersection of Two SetsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the intersection of the two sets.1) {1, 10, 5, 8}∩{5, 11, 1}A) {1, 5}B) {1}C) {1, 5, 8, 10, 11}D)∅2) {1, 10, 8}∩{5, 11}A)∅B) {10, 8}C) {1, 5, 8, 10, 11}D) {1, 8}3) {7, 9, 10, 12}∩∅A)∅B) {7, 9, 10, 12}C) {7, 9}D) {10, 12}4Find the Union of Two SetsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the union of the two sets.1) {2, 5, 8, 11}∪{2, 5, 13}A) {2, 5, 8, 11, 13}B) {2, 5}C) {8, 11, 13}D)∅2) {1, 11}∪{1, 4, 9}A) {1, 4, 9, 11}B) {1}C) {4, 9, 11}D)∅3) {3, 5, 6, 8}∪∅A) {3, 5, 6, 8}B) {3, 5}C) {6, 8}D)∅Page 2

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5Recognize Subsets of the Real NumbersMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.List all numbers from the given set B that are members of the given Real Number subset.1) B={18,6,-15, 0, 0.6,25} IntegersA) 18,-15, 0,25B) 18, 0C) 18,-15, 0D) 18, 0,252) B={4,6,-21, 0, 0.4,9} Whole numbersA) 4, 0,9B) 4,-21, 0C) 4,-21, 0,9D) 4, 03) B={6,5,-22, 0, 0.4,25} Natural numbersA) 6,25B) 6, 0,25C) 6, 0D) 64) B={11,8,-18, 0, 34 ,4, 0.6, 0.61} Rational numbersA) 11,-18, 0, 34 ,4, 0.61, 0.6B) 11, 0,4C)8,4D)8, 34 , 0.615) B={9,8,-5, 0, 67 ,4, 0.5, 0.35}Irrational numbersA)8B)8, 0.5C)8,4, 0.5D)8,4, 0.356) B={17,7, 0, 23 ,9,-0.2, 0.95,-7}Real numbersA) 17,7, 0, 23 ,9,-0.2, 0.95,-7B) 17,7, 0, 23 ,9, 0.95C) 17,7, 23 ,9,-0.2, 0.95,-7D) 17, 0, 23 ,-0.2, 0.95,-76Use Inequality SymbolsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine whether the statement is true or false.1) 6>9A) FalseB) True2) 18≥4A) TrueB) False3)-67<0A) TrueB) False4) 9<-7A) FalseB) True5) 18≤12A) FalseB) TruePage 3

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6)-13≤22A) TrueB) False7) 20>11A) TrueB) False8)-7≥23A) FalseB) True9)π≤πA) TrueB) False10)π>3A) TrueB) False7Evaluate Absolute ValueMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Rewrite the expression without absolute value bars.1) |20|A) 20B)-20C) 40D) 02) |-22|A) 22B)-22C) 44D) 03) 131A) 13B)-1C) 1D)-134)13-15A) 15-13B)13-15C)-2D) 25) |12+(-14)|A) 2B) 26C)-2D)-266)-8--9A) 1B) 17C)-1D)-177)-7+-9A) 16B) 2C)-2D)-16Evaluate the expression for the given values of x and y.8) |x|x+|y|y;x=4 and y=-1A) 0B) 2C) 1D)-1Page 4

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8Use Absolute Value to Express DistanceMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Express the distance between the given numbers using absolute value. Then find the distance by evaluating theabsolute value expression.1) 13 and 77A) |13-77|=64B)-|77-13|= -64C) |13+77|=90D)-|13+77|= -902)-98 and-40A) |(-98)-(-40)|=58B) |(-40)-(-98)|= -58C) |(-40)+(-98)|=-138D) |-(-98)+(-40)|=1383) 31 and-30A) |31-(-30)|=61B) |(-30)-31|= -61C) |31+(-30)|=1D) |-31+(-30)|= -14) 3.3 and 21.6A) |3.3-21.6|=18.3B) |21.6-3.3|= -18.3C) |3.3+21.6|=24.9D) |-3.3+21.6|= -24.95)-24.9 and 20.3A) |-24.9-20.3|=45.2B) |20.3+(-24.9)|=-45.2C) |20.3-(-24.9)|=-4.6D) |-24.9+(-20.3)|=4.66) 39.4 and 20.4A) |39.4-20.4|=19.0B) |20.4-39.4|= -19.0C) |20.4+39.4|=59.8D)-|39.4+20.4|= -59.89Identify Properties of the Real NumbersMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.State the name of the property illustrated.1) 5+(-3)=(-3)+5A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Identity property of addition2) 14·(7+1)=14·7+14·1A) Distributive property of multiplication over additionB) Commutative property of multiplicationC) Associative property of multiplicationD) Commutative property of addition3) 2+(21+22)=(2+21)+22A) Associative property of additionB) Commutative property of additionC) Distributive property of multiplication over additionD) Identity property of additionPage 5

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4) (4+7)+1=(7+4)+1A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Inverse property of addition5) 4·(9·18)=4·(18·9)A) Commutative property of multiplicationB) Associative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication6) (8+2)+(6+18)=(6+18)+(8+2)A) Commutative property of additionB) Associative property of additionC) Distributive property of multiplication over additionD) Inverse property of addition7) 9·(17·2)=(17·2)·9A) Commutative property of multiplicationB) Associative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication8) (3·19)·9=3·(19·9)A) Associative property of multiplicationB) Commutative property of multiplicationC) Distributive property of multiplication over additionD) Identity property of multiplication9) 7(x+5)=7x+7·5A) Distributive property of multiplication over additionB) Commutative property of multiplicationC) Associative property of multiplicationD) Identity property of multiplication10) 5(-6+9)=-30+45A) Distributive property of multiplication over additionB) Associative property of multiplicationC) Associative property of additionD) Commutative property of multiplication11)-6(4+6)=-24+(-36)A) Distributive property of multiplication over additionB) Associative property of multiplicationC) Associative property of additionD) Commutative property of multiplication12)1(x+2) (x+2)=1, x≠-2A) Inverse property of multiplicationB) Inverse property of additionC) Commutative property of multiplicationD) Identity property of multiplicationPage 6

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13) (x+7)+[-(x+7)]=0A) Inverse property of additionB) Inverse property of multiplicationC) Commutative property of additionD) Identity property of multiplication10Simplify Algebraic ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the algebraic expression.1)-7(2r+6)+4(6r+5)A) 10r-22B)-5r-1C) 10r+6D)-56r2) (8z+10)-(3z-8)A) 5z+18B) 5z+2C) 11z+18D) 5z-183)-5(2x-7)-4x+5A)-14x+40B) 6x+40C) 14x+40D)-14x-30Write the algebraic expression without parentheses.4)-(47w)A)-47wB) 47wC)-47-wD) 47-w5)-5(5z)A)-25zB) 25zC)-25-5zD)-25+z6)-(7x-7)A)-7x+7B) 7x-7C)-7x-7D) 49x7)-(-3+4y)A) 3-4yB) 3+4yC)-3+4yD) 12y8)-(7z-8w+8y)A)-7z+8w-8yB)-7z+8w+8yC)-7z-8w+8yD)-7z-8w-8y9) 14 (4x)+[(3x)+(-3x)]A) xB) 7xC)-5xD) 10.2Exponents and Scientific Notation1Use the Product RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 54·53A) 57B) 512C) 257D) 25122) x·x3A) x4B) 2x3C) x3D) 2x43) x3·x9A) x12B) x27C) 12xD) 27xPage 7

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4) (-6x7)(-4x9)A) 24x16B)-24x16C) 24x63D)-24x635) (-10x4y)(-4x5y2)A) 40x9y3B)-40x9y2C)-14x9y2D) 40x20y22Use the Quotient RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 2827A) 2B) 12C) 128D) 872) x6x2A) x4B) x8C) x2D)1x43) x4x7A)1x3B)-x3C) x3D)-1x34) 5x5x3A) 5x2B) 25x2C) 5x8D) 10x5) 27x133x3A) 9x10B) x9C) x10D) 9x96) x13y13x7y4A) x6y9B) x5y8C) xy9D) x5y97) 72x5y119x2y5A) 8x3y6B) x3y6C) 8x2y3D) 8x2y5Page 8

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8)-14x22x7A)-7x5B)-7x5C)-7x4D)-7x49) 30x11y10z65x3y4z5A) 6x8y6zB) x8y6zC) 6x7y5zD) 6x8y63Use the Zero-Exponent RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 40A) 1B)-1C) 0D) 42) (-8)0A) 1B)-1C) 0D) 83)-70A)-1B) 1C) 0D) 74) x6y0A) x6B) 1C) 0D)1x65)-9y0A)-9B) 1C) 0D)-86) (15b)0A) 1B) 0C) bD) 157)-45x9y59x4y20A) 1B) x5y3C)-5x5y3D) 04Use the Negative-Exponent RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) 2-3A) 18B)-8C) 8D) 162) (-3)-2A) 19B)-9C) 9D)-19Page 9

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3)-5-4A)-1625B)-625C) 625D)1204) 2-3·2A) 14B) 18C) 4D) 85) 23·2-4A) 12B)-2C) 128D)-126) x6·x-2A) x4B)1x4C)-x4D)-1x47) x-5·x2A)1x3B)-x3C) x3D)-1x38) x2y-3A) x2y3B) y3x2C)x2y13D) y13x29) 6x-6y2A) 6y2x6B)6x6y2C)y26x6D) 6x6y210) x-9x2A)1x11B)1x18C)1x7D) x1111) x-4y-4A) y4x4B)1x4y4C) x4y4D) x4y412) x4y-5z-9A) x4z9y5B)z9x4y5C)y5x4z9D) x4z5y9Page 10

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13) 63x20y57x19y-3A) 9xy8B) 63xy8C) 9x39y8D) 9xy25Use the Power RuleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) (23)4A) 4096B) 128C) 24D) 322) (34)-2A)16561B)1729C)-24D)-1623) (x5)9A) x45B) x14C) 9x5D) 9x454) (x-7)8A)1x56B)-x56C)-7x8D)-7x565) (x4)-8A)1x32B)-x32C)-8x4D)-8x326) (x-3)-3A) x9B)1x9C)1x6D)-x66Find the Power of a ProductMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1) (2x)5A) 32x5B) 10xC) 32xD) 10x52) (-2x)6A) 64x6B)-12xC) 64xD)-12x63) (11x7)2A) 121x14B) 11x14C) 121x7D) 11x94) (x8y)2A) x16y2B) x16yC) x10y3D) x10yPage 11

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5) (-6x3y6)2A) 36x6y12B)-6x6y12C)-36x6y12D) 36x5y86) (5x3)-2A)125x6B)15x6C) 25x6D) 25x67) (x-4y5)-2A)x8y10B) x-6y3C)1x8y10D)y3x-68) (5x-6y3z-2)-3A) x18z6125y9B)y6125x9z5C)x18z6-15y-9D)y6-15x9z57Find the Power of a QuotientMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression.1)x93A)x3729B)x46561C) x9D) x392)-6x2A)36x2B)-36x2C)36xD)6x23)x244A)x8256B) x84C)x6256D) x644)-3xy3A)-27x3y3B)-27xy3C)-9x3y3D)-9xy5)4x2y3z43A) 64x6y9z12B) 4x6y9z12C) 64x5y6z7D) 4x6y9z7Page 12

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6)-8x8y74x14y-23A)-8y27x18B) 8y27x18C)-8y15x18D)-8x18y277)x-2y6-4A) x8y24B) x-6y2C)1x8y24D)y2x-68)4x3y2-4A)y8256x12B) 256x12y8C) 256y8x12D)y2256x128Simplify Exponential ExpressionsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the exponential expression. Assume that variables represent nonzero real numbers.1) 23·5A) 40B) 30C) 1000D) 132) (-4)3A)-64B) 64C)-12D) 123)-32A)-9B) 6C) 9D)-64) (2x2)3x15A)8x9B)2x9C)8x10D)8x215) (-2x4y-5)(5x-1y)A)-10x3y4B)-10x3y6C) 3x3y4D)-10x5y66) 2-8x-1y42-5x-4y8A)x38y4B)18x4y4C) 3x3y4D)8x3y4Page 13

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7)xy6x6y-2A) x10y10B)1x8y13C)1x14y14D) y10x108)9x-5y-2z33xy-2z-3-1A)x63z6B)x43z6C) 3x6z6D) x6y43z69Use Scientific NotationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Write the number in decimal notation without the use of exponents.1) 3×10-2A) 0.03B) 300C) 0.3D) 302) 8×105A) 800,000B) 0.00008C) 8,000,000D) 0.0000083) 2.87×104A) 28,700B) 287,000C) 2870D) 114.84) 9.33×10-4A) 0.000933B) 0.00933C) 0.0000933D)-933,0005) 2.408×10-6A) 0.000002408B) 0.00002408C) 0.0000002408D)-2,408,0006)-7.19×106A)-7,190,000B)-71,900,000C)-719,000D) 7,190,0007)-4.0032×107A)-40,032,000B)-400,320,000C)-4,003,200D)-280.224Write the number in scientific notation.8) 6912A) 6.912×103B) 6.912×104C) 6.912×10-3D) 6.912×1019) 290,000A) 2.9×105B) 2.9×10-5C) 2.9×106D) 2.9×10-610) 2,800,000A) 2.8×106B) 2.8×10-6C) 2.8×107D) 2.8×10-711) 5,023,260A) 5.02326×106B) 5.02326×107C) 5.02326×10-6D) 5.02326×101Page 14

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12) 0.000939A) 9.39×10-4B) 9.39×104C) 9.39×10-5D) 9.39×10-313) 0.00009958A) 9.958×10-5B) 9.958×105C) 9.958×10-4D) 9.958×10414) 0.0000000717013A) 7.17013×10-8B) 7.17013×108C) 7.17013×10-7D) 7.17013×10-9Perform the indicated computation. Write the answer in scientific notation.15) (4×103)(4.8×104)A) 1.92×108B) 19.2×108C) 192×107D) 1.92×101216) (4×10-3)(1.5×10-1)A) 6×10-4B) 6×10-3C) 60×10-4D) 6×10317) 16×10-84×10-6A) 4×10-2B) 4×10-14C) 8×10-2D) 8×10-1418) 17.08×10-84×105A) 4.27×10-13B) 4.27×10-3C) 8.54×10-13D) 8.54×10-319) 8.82×1062.1×103A) 4.2×103B) 4.2×109C) 8.4×103D) 8.4×10920) 450,000,000,000,0000.00000009A) 5×1021B) 5×1020C) 36×1021D) 36×102021) 0.00016×0.00030.0008A) 6×10-5B) 6×105C) 48×106D) 48×10-6Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places.22) In a state with a population of 9,000,000 people, the average citizen spends $6,000 on housing each year.What is the total spent on housing for the state?A) $5.4×1010B) $5.4×109C) $54×1011D) $54×101023) Approximately 9×103 employees of a certain company average $30,000 each year in salary. What is thetotal amount earned by all the employees of this company per year?A) $2.7×108B) $27×108C) $2.7×109D) $27×109Page 15

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0.3Radicals and Rational Exponents1Evaluate Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression or indicate that the root is not a real number.1)4A) 2B) 16C) 14D) Not a real number2)-9A)-3B) 3C)-4D) Not a real number3)-121A)11121B) 14,641C) 11D) Not a real number4)144+25A) 13B) 17C) 169D)1195)100-36A) 8B) 14C) 64D)286)16+9A) 7B) 5C) 25D)72Simplify Expressions of the Form SqRt(a^2)MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression or indicate that the root is not a real number.1)(5)2A) 5B) 625C)125D) Not a real number2)(-4)2A) 4B) 16C)-4D) Not a real number3Use the Product Rule to Simplify Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the product rule to simplify the expression.1)147A) 73B) 37C) 21D) 122)10A)10B) 52C) 25D) 23)275A) 511B)275C) 55D) 2511Page 16

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4)486x2A) 9 x6B) 96xC) 486xD) 6x295)98x2A) 7 x2B) 72x2C) 7x22D) 726)9x·45xA) 9 x5B) 95xC) 9x25D) 95x27)14x2·28xA) 14 x2xB) 14 x2C) 14x22xD) 14 x2x2Solve the problem.8) Racing cyclists use the algebraic expression 4x to determine the maximum speed, in miles per hour, toturn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist shouldtravel around a corner of radius 11 feet without tipping over. Write the answer in simplified radical form.A) 411 miles per hourB) 122 miles per hourC) 12+2 miles per hourD) 4(3+2)xmiles per hour9) The formula v=2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on acurved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at anexit ramp as 160 feet. What is the maximum safe speed?A) 20 miles per hourB) 16 miles per hourC) 25 miles per hourD) 17 miles per hour10) The formula v=20L can be used to estimate the speed of a car, v, in miles per hour, based on the length,L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accidentand its skid marks measure 101.25 feet, at what estimated speed was the car traveling when it applied itsbrakes just prior to the accident?A) 45 miles per hourB) 50 miles per hourC) 40 miles per hourD) 55 miles per hour11) The average height of a boy in the United States, from birth through 60 months, can be modeled byy=2.9x+20.1 where y is the average height, in inches, of boys who are x months of age. What would bethe expected difference in height between a child 49 months of age and a child 16 months of age?A) 8.7 inchesB) 48.9 inchesC) 20.3 inchesD) 10.7 inches4Use the Quotient Rule to Simplify Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the quotient rule to simplify the expression.1)19A) 13B)181C) 3D) 9Page 17

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2)49A) 23B) 0C)23D)233)72x32xA) 6 xB) 6 x2C) 2x2D) 6x224)100x45xA) 2 x5xB) 100x3C) 5 xxD) x21005Solve the problem.5) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic expressiond16 . Find how long it will take a ball dropped from the top of a building 38 feet tall to hit the ground.Write the answer in simplified radical form.A)384secondsB) 624secondsC)3816secondsD) 6+24seconds5Add and Subtract Square RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Add or subtract terms whenever possible.1) 46+86A) 126B) 3212C) 1212D)-462) 93+675A) 393B) 213C) 153D)-3933) 63x+83xA) 143xB) 486xC) 14x6D)-234)-25-845A)-265B)-225C)-105D) 2655)-975+6147-3192A)-273B)-93C)-693D) 6936)64+300+49+243A) 193+15B) 193+64+49C)300+243+15D) 1813+157)3x+412x+327xA) 183xB) 1842xC) 742xD) 73xPage 18

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6Rationalize DenominatorsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Rationalize the denominator.1)129A)2929B)29C) 1+29D) 1+29292)22A)2B) 22C) 2D) 13)817A) 977B) 97C) 8177D) 584)14411A) 121111B) 1211C) 1441111D) 1335)73A)213B)219C)21D)76)78-6A) 56+7658B) 56-7658C) 56+762D) 78-767)617+2A)102-2613B)102+2613C)102-2619D) 3102+173468)37-2A) 21+3247B) 21-3247C) 21+325D) 37-329)25+7A)7-5B)5-7C)7+5D)2Page 19

Test Bank for College Algebra Essentials, 5th Edition - Page 21 preview image

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7Evaluate and Perform Operations with Higher RootsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the radical expressions or indicate that the root is not a real number.1) 3-27A)-3B) 3C)-27D) not a real number2) 3 (4)3A) 4B)-4C) 64D) not a real number3) 4 16A) 2B)-2C) 16D) not a real number4) 4 (-10)4A) 10B)-10C) 10,000D) not a real numberSimplify the radical expression.5) 3 x5A) x 3 x2B) x2 3 x2C) x 3 xD) x2 3 x6) 3 10·3 4A) 2 3 5B) 3 40C) 2 3 10D) 6 40Add or subtract terms whenever possible.7) 3 3 81+3 24A) 11 3 3B) 3 3 105C) 4 3 105D) 5 3 38) y 3 54x-3 250xy3A)-2y 3 2xB) 3y 3 2x-54 3 2xy3C) (y+1) 3 255D) y 3-245xy38Understand and Use Rational ExponentsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Evaluate the expression without using a calculator.1) 91/2A) 3B) 6C) 1.5D) 122) 2561/4A) 4B) 16C) 64D) 10243) 84/3A) 16B) 64C) 32D) 128Page 20

Test Bank for College Algebra Essentials, 5th Edition - Page 22 preview image

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4) 16-3/2A)164B)-164C) 64D)-64Simplify using properties of exponents.5) (6x1/3)(3x3/2)A) 18x11/6B) 18x2/3C) 18x11/5D) 18x1/36) 100x2/310x1/4A) 10x5/12B) 10x1/12C) 90x1/12D) 10x5/37) (81x10y4)1/2A) 9x5y2B) 6561x20y4C) 92 x5y2D) 81x5y2Simplify by reducing the index of the radical.8) 15 x9A) 5 x3B) 3 x3C) 5 xD) 3 x9) 12 81x4A) 3 3xB) 4 3xC) 3 3 3xD)127xSolve the problem.10) The algebraic expression 0.07d3/2 describes the duration of a storm, in hours, whose diameter is d miles.Use a calculator to determine the duration of a storm with a diameter of 12 miles. Round to the nearesthundredth.A) 2.91 hoursB) 0.24 hoursC) 41.57 hoursD) 0.77 hours0.4Polynomials1Understand the Vocabulary of PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Is the algebraic expression a polynomial? If it is, write the polynomial in standard form.1) 2x-1+5+6xA) NoB) Yes; 6x+2x-1+52) 6x-7+2x2A) Yes; 2x2+6x-7B) No3) 3x-7xA) NoB) Yes; 7x-3Page 21

Test Bank for College Algebra Essentials, 5th Edition - Page 23 preview image

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4) x2+x4-x3-3A) Yes; x4-x3+x2-3B) NoFind the degree of the polynomial.5) 4x-7x6-9A) degree 6B) degree 7C) degree 4D) degree-76)-9x+2x7-3x6-6A) degree 7B) degree 4C) degree 2D) degree 67)-6x3-3x2-2x-2x4-5A) degree 4B) degree 3C) degree-6D) degree 28) x4-9x3y5+12xy-10x+8A) degree 8B) degree 4C) degree 14D) degree-92Add and Subtract PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Perform the indicated operations. Write the resulting polynomial in standard form.1) (7x5+2x2-8x)+(4x5+3x2+5x)A) 11x5+5x2-3xB)-4x5+10x2+7xC) 11x+5x5-3x2D) 13x82) (9x7+2x6+6x5+4)+(9x7+7x6-8x5-6)A) 18x7+9x6-2x5-2B) 18x14+9x12-2x10-2C) 25x36-2D) 11x7+11x6+3x5+113) (-6x6+17x3+7)+(9x6+13x3+9)A) 3x6+30x3+16B) 3x6+19x3+2C) 3x6+30x3+2D) 49x94) (-8x5-9x4-3x3-3)+(2x5+7x4+9x3+6)A)-6x5-2x4+6x3+3B) 10x5+16x4+12x3+9C)-6x5+16x4+12x3+9D) 10x5+16x4+12x3+35) (5x7+14x4+17)-(2x7-14x4+20)A) 3x7+28x4-3B) 3x7+16x4+37C) 3x7+28x4+37D) 28x116) (6x4+8x3-5x2+5)-(2x4+3x3-7x2-6)A) 4x4+5x3+2x2+11B) 8x4+11x3-12x2-1C) 4x4+11x3-12x2-1D) 8x4+11x3-12x2+117) (2x6+2x5+3)-(7x6-11x5-20)A)-5x6+13x5+23B)-5x6+9x5-17C)-5x6+13x5-17D) 31x118) (2x2+4x+7)+(2x2+9x+3)-(5x+2)A) 4x2+8x+8B) 4x2+8x+12C) 2x2+8x+8D) 2x2+8x+12Page 22

Test Bank for College Algebra Essentials, 5th Edition - Page 24 preview image

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3Multiply PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x-3)(x2+3x+9)A) x3-27B) x3+27C) x3-6x2-6x-27D) x3+6x2+6x-272) (x-11)(x2+8x-6)A) x3-3x2-94x+66B) x3+19x2+82x-66C) x3-3x2-82x-66D) x3+19x2+94x+663) (x+9)(x2+4x-7)A) x3+13x2+29x-63B) x4+9x3+4x2+29x-63C) x3+13x2+43x-63D) x3+13x2+43x+634) (x+6)(5x2+3x+7)A) 5x3+33x2+25x+42B) 5x3+30x2+18x+42C) 35x3+21x2+49xD) 90x4+5x3+126x2+425) (7x-1)(x2-2x+1)A) 7x3-15x2+9x-1B) 7x3-13x2+5x-1C) 7x3-14x2+7x+1D) 7x3+15x2-9x+14Use FOIL in Polynomial MultiplicationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x+11)(x+7)A) x2+18x+77B) x2+77x+18C) x2+17x+77D) x2+18x+182) (3x+1)(x+10)A) 3x2+31x+10B) x2+10x+31C) 3x2+30x+10D) x2+31x+303) (9x+11)(5x+4)A) 45x2+91x+44B) 14x2+91x+44C) 45x2+91x+91D) 14x2+91x+914) (2x2-9)(6x2+5)A) 12x4-44x2-45B) 8x4-44x2-45C) 12x4-44x2-44D) 12x2-44x-455) (7x3-4)(x2+3)A) 7x5+21x3-4x2-12B) 7x5+17x3-12C) 7x5+17x2-12D) 7x6+21x3-4x2-12Page 23

Test Bank for College Algebra Essentials, 5th Edition - Page 25 preview image

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Solve the problem.6) Write a polynomial in standard form that represents the volume of the open box.x12-8x6-8xA) 64x3-144x2+72xB) 64x3+144x2+72xC) 64x2-144x+72D) 8x3-144x2+72x7) Write a polynomial in standard form that represents the area of the shaded region.x+9x+6x+3x+2A) 4x+15B) 20x+39C) x2+19x+15D)-4x-155Use Special Products in Polynomial MultiplicationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the product.1) (x+4)(x-4)A) x2-16B) x2-8C) x2-8x-16D) x2+8x-162) (3x+8)(3x-8)A) 9x2-64B) x2-64C) 9x2-48x-64D) 9x2+48x-643) (5+6x)(5-6x)A) 25-36x2B) 25-60x-36x2C) 36x2-25D) 25+60x-36x24) (4x2+7x)(4x2-7x)A) 16x4-49x2B) 16x4-56x3-49x2C) 8x4-14x2D) 16x4+56x3-49x25) (1+x4)(1-x4)A) 1-x8B) 2-x8C) 2-x16D) 1-x16Page 24

Test Bank for College Algebra Essentials, 5th Edition - Page 26 preview image

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6) (12-y4)(12+y4)A) 144-y8B) 144-y16C) 144-y4D) y8-1447) (x+15)2A) x2+30x+225B) x2+225C) 225x2+30x+225D) x+2258) (x-14)2A) x2-28x+196B) x2+196C) 196x2-28x+196D) x+1969) (9x+5)2A) 81x2+90x+25B) 81x2+25C) 9x2+90x+25D) 9x2+2510) (3x-10)2A) 9x2-60x+100B) 9x2+100C) 3x2-60x+100D) 3x2+10011) (3x2+4)2A) 9x4+24x2+16B) 9x2+24x+16C) 3x4+24x2+16D) 9x4+1612) (7x2-4)2A) 49x4-56x2+16B) 49x4+56x2+16C) 49x4-56x2-16D) 49x2-56x+1613) (6+7x)2A) 36+84x+49x2B) 36+49x2C) 36x2+84x+49D) 36+84x+7x214) (7-9x)2A) 49-126x+81x2B) 49+81x2C) 49x2-126x+81D) 49-126x-81x215) (x-3)3A) x3-9x2+27x-27B) x3-3x2+15x-27C) x3-9x2+15x-27D) x3-9x2+9x-2716) (2x+5)3A) 8x3+60x2+150x+125B) 8x3+60x2+60x+125C) 4x6+10x3+15,625D) 4x2+20x+2517) (3x-4)3A) 27x3-108x2+144x-64B) 27x3-108x2+108x-64C) 27x3+108x2+144x+64D) 9x2-24x+166Perform Operations with Polynomials in Several VariablesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Perform the indicated operations.1) (-9x2y-xy)+(4x2y+7xy)A)-5x2y+6xyB) 13x2y+8xyC)-5x2y+8xyD) 13x2y+6xyPage 25

Test Bank for College Algebra Essentials, 5th Edition - Page 27 preview image

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2) (12x2y-8xy+4)+(-11x2y+3xy-9)A) x2y-5xy-5B)-x2y-11xy+13C)-5x3y2-5D) 23x2y+11xy+133) (5x4y2-3x2y2+10xy)+(7x4y2-2x2y2+9xy)A) 12x4y2-5x2y2+19xyB)-5x4y2+12x2y2+19xyC) 12x4y2+5x2y2+19xyD) 5x4y2-12x2y2+19xy4) (x3+4xy-9y2)-(3x3+9xy+y2)A)-2x3-5xy-10y2B) 4x3-5xy-10y2C)-2x3-5xy-8y2D) 2x3+5xy-8y25) (9x4+3xy-y3)-(x4+5xy+3y3)A) 8x4-2xy-4y3B) 10x4+13xy+2y3C) 9x4-2xy-4y3D) 8x4-2xy-2y36) (11x4y2+9x3y+12y)-(5x4y2+4x3y+2y+6x)A) 6x4y2+5x3y+10y-6xB) 16x4y2+13x3y+14y+6xC) 6x4y2-5x3y+10y-6xD) 6x4y2+5x3y+10y+6xFind the product.7) (x-7y)(x-2y)A) x2-9xy+14y2B) x-9xy+14yC) x2-9xy-9y2D) x2-12xy+14y28) (x+4y)(2x-3y)A) 2x2+5xy-12y2B) x2+5xy-12y2C) 2x2+5xy+5y2D) x2+5xy+5y29) (3xy-10)(9xy+5)A) 27x2y2-75xy-50B) 12x2y2-75xy-50C) 27x2y2-75xy-75D) 12x2y2-75xy-7510) (5x+8y)2A) 25x2+80xy+64y2B) 25x2+64y2C) 5x2+80xy+64y2D) 5x2+64y211) (8x-11y)2A) 64x2-176xy+121y2B) 64x2+121y2C) 8x2-176xy+121y2D) 8x2+121y212) (m-n)(m2+mn+n2)A) m3-n3B) m3+n3C) m3-2m2n-2mn2-n3D) m3+2m2n+2mn2-n313) (x2y2+3)2A) x4y4+6x2y2+9B) x2y2+6xy+9C) x4y4+3x2y2+9D) x4y4+914) (3x+7y)(3x-7y)A) 9x2-49y2B) 3x2-7y2C) 9x2-42xy-49y2D) 9x2+42xy-49y2Page 26

Test Bank for College Algebra Essentials, 5th Edition - Page 28 preview image

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15) (3xy2-13y)(3xy2+13y)A) 9x2y4-169y2B) 3x2y4-13y2C) 9x2y4-78xy3-169y2D) 9x2y4+78xy3-169y20.5Factoring Polynomials1Factor Out the Greatest Common Factor of a PolynomialMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor out the greatest common factor.1) 5x-20A) 5(x-4)B) 5(x-20)C) 5x(x-4)D) 5x(-4)2) 5x2+30xA) 5x(x+6)B) x(5x+30)C) 5(x2+6x)D) 5x(x+6x)3) 14x4-6x3+10x2A) 2x2(7x2-3x+5)B) 2(7x4-3x3+5x2)C) x2(14x2-6x+10)D) 2x(7x3-3x2+5x)4) x(x+12)+13(x+12)A) (x+12)(x+13)B) (x2+12x)+(13x+156)C) 13x(x+12)D) 12x(x+13)5) x(5x-3)-5(5x-3)A) (5x-3)(x-5)B) (5x-3)(x+5)C) (5x-5)(x-3)D)-5x(5x-3)6) x2(x-11)-(x-11)A) (x-11)(x2-1)B) (x-11)(x2+1)C) x2(x-11)D) (x3-11x2)-(x-11)2Factor by GroupingMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor by grouping. Assume any variable exponents represent whole numbers.1) x3-4x2+2x-8A) (x-4)(x2+2)B) (x+2)(x2-4)C) (x+4)(x2-2)D) (x-4)(x+2)2) x3+7x-5x2-35A) (x-5)(x2+7)B) (x+5)(x2+7)C) (x-5)(x2-7)D) (x-5)(x+7)3) 2x3-10x2+9x-45A) (x-5)(2x2+9)B) (x+5)(2x2+9)C) (x-5)(2x2-9)D) (x-5)(2x+9)Page 27

Test Bank for College Algebra Essentials, 5th Edition - Page 29 preview image

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3Factor TrinomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the trinomial, or state that the trinomial is prime.1) x2-12x+27A) (x-3)(x-9)B) (x+3)(x-9)C) (x+3)(x+1)D) prime2) x2+14x+48A) (x+6)(x+8)B) (x-6)(x+8)C) (x-6)(x+1)D) prime3) x2-16x+63A) (x-9)(x-7)B) (x+9)(x-7)C) (x+9)(x+1)D) prime4) x2+5x-36A) (x+9)(x-4)B) (x-9)(x+4)C) (x-9)(x+1)D) prime5) x2-x-6A) (x+2)(x-3)B) (x+3)(x-2)C) (x+1)(x-5)D) prime6) x2-x-54A) (x-54)(x+1)B) (x+6)(x-9)C) (x-6)(x+9)D) prime7) 7x2+36x+32A) (7x+8)(x+4)B) (7x+4)(x+8)C) (7x+8)(7x+4)D) prime8) 5x2-39x+28A) (5x-4)(x-7)B) 5(x-4)(x-7)C) (5x+7)(x-4)D) (5x-4)(5x+7)9) 2x2-7x-15A) (2x+3)(x-5)B) (2x-5)(x+3)C) (2x-3)(x+5)D) prime10) 7x2-5x+2A) (7x+2)(x-1)B) (7x-1)(x+2)C) (7x-2)(x+1)D) prime11) 10x2+23x+12A) (2x+3)(5x+4)B) (2x-3)(5x-4)C) (10x+3)(x+4)D) prime12) 10x2-23x+12A) (2x-3)(5x-4)B) (2x+3)(5x+4)C) (10x+3)(x+4)D) prime13) 10x2+11x-6A) (2x+3)(5x-2)B) (2x-3)(5x+2)C) (10x+3)(x-2)D) prime14) x2-15xy+54y2A) (x-9y)(x-6y)B) (x+9y)(x-6y)C) (x+9y)(x+y)D) prime15) 9x2+10xy+y2A) (9x+y)(x+y)B) (9x-y)(x-y)C) (9x+y)(x+9y)D) primePage 28

Test Bank for College Algebra Essentials, 5th Edition - Page 30 preview image

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16) 5x2-2xy-16y2A) (5x+8y)(x-2y)B) (5x+2y)(x-8y)C) y(5x+8)(x-2)D) prime17) 12x2-25xy+12y2A) (3x-4y)(4x-3y)B) (3x+4y)(4x+3y)C) (12x-4y)(x-3y)D) prime4Factor the Difference of SquaresMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the difference of two squares.1) x2-144A) (x+12)(x-12)B) (x+12)2C) (x-12)2D) prime2) 4x2-49A) (2x+7)(2x-7)B) (2x-7)2C) (2x+7)2D) prime3) 81x2-121y2A) (9x+11y)(9x-11y)B) (9x-11y)2C) (9x+11y)2D) prime4) x4-81A) (x2+9)(x+3)(x-3)B) (x2+9)(x2+9)C) (x2-9)(x2-9)D) prime5) (16x4-81)A) (4x2+9)(2x+3)(2x-3)B) (4x2+9)(4x2-9)C) (2x+3)2(2x-3)2D) (4x2+9)(4x2+9)5Factor Perfect Square TrinomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor the perfect square trinomial.1) x2+4x+4A) (x+2)2B) (x-2)2C) (x+2)(x-2)D) prime2) x2-15x+225A) (x-15)2B) (x+15)2C) (x+15)(x-15)D) prime3) 49x2+14x+1A) (7x+1)2B) (7x+1)(7x-1)C) (x+7)2D) primePage 29

Test Bank for College Algebra Essentials, 5th Edition - Page 31 preview image

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6Factor the Sum or Difference of Two CubesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor using the formula for the sum or difference of two cubes.1) x3-8A) (x-2)(x2+2x+4)B) (x+2)(x2-2x+4)C) (x+8)(x2-1)D) prime2) x3+125A) (x+5)(x2-5x+25)B) (x-5)(x2+5x+25)C) (x+5)(x2+25)D) prime3) 125x3-1A) (5x-1)(25x2+5x+1)B) (5x-1)(25x2+1)C) (5x+1)(25x2-5x+1)D) prime4) 125x3+1A) (5x+1)(25x2-5x+1)B) (5x-1)(25x2+1)C) (5x-1)(25x2+5x+1)D) prime5) 27x3+64A) (3x+4)(9x2-12x+16)B) (3x-4)(9x2+12x+16)C) (3x+4)(9x2+12x+16)D) (3x+4)(9x2+16)6) 125x3-27A) (5x-3)(25x2+15x+9)B) (5x+3)(25x2-15x+9)C) (5x-3)(25x2-15x+9)D) (5x-3)(25x2+9)7Use a General Strategy for Factoring PolynomialsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Factor completely, or state that the polynomial is prime.1) 3x3-108xA) 3x(x+6)(x-6)B) 3(x+6)(x2-6x)C) x(x+6)(3x-18)D) prime2) 98x2-18A) 2(7x+3)(7x-3)B) 2(7x-3)2C) 2(7x+3)2D) prime3) 2x2+6x+4A) 2(x+2)(x+1)B) (2x+4)(x+1)C) (x+2)(2x+2)D) 2(x2+3x+2)4) 2x4-2A) 2(x2+1)(x+1)(x-1)B) 2(x2+1)(x2-1)C) 2(x+1)2(x-1)2D) primePage 30

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