College Algebra, 3rd Edition Test Bank

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ExamName___________________________________SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Factor usingu-substitution.1)36 +x4- 13x21)Answer:(x+ 2)(x- 2)(x+ 3)(x- 3)Explanation:Graph the elements of the set on a number line.2)-3.5, -134, 3.25, -3, -0.8,ʌ,92,362)Answer:Explanation:Rewrite the expression using the associative property of multiplication and simplify, if possible.3)-8Â-38x3)Answer:-8-38x= 3xExplanation:The costC, in millions of dollars, for a government to find and seizeP% of an illegal drug is modeled bythe rational equationC=350P100 -P(0P< 100).4)Why does the cost increase dramatically the closer you get to 100%?4)Answer:It would require many resources.Explanation:Find the indicated sum.5)(7d2+ 2d- 4) + (-10d2- 10d- 3)5)Answer:-3d2- 8d- 7Explanation:1

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Factor out the common binomial factor.6)Factor out the common binomial factor.5x(x- 6)- 7(x- 6)6)Answer:(5x- 7)(x- 6)Explanation:Identify as either true or false. If false, state why.7)R2N7)Answer:False. Not all real numbers are natural numbers.Explanation:Factor the trinomial completely.8)5x2+ 48x+ 648)Answer:(5x+ 8)(x+ 8)Explanation:Translate the phrase into an algebraic expression.9)ninetimes the sum of a number andfive, decreased byone9)Answer:9(n+5) -1Explanation:The costC, in millions of dollars, for a government to find and seizeP% of an illegal drug is modeled bythe rational equationC=350P100 -P(0P< 100).10)Will 100% of the drugs ever be seized?10)Answer:NoExplanation:List all the numbers in the set that are elements of Z.11)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3611)Answer:{36}Explanation:Compute the product.12)(x+ 2)(x+ 3)(x+ 4)12)Answer:x3+ 9x2+ 26x+ 24Explanation:Factor the perfect square trinomial completely.13)x2- 18x+ 8113)Answer:(x- 9)2Explanation:2

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Evaluate without a calculator, using the order of operations.14)542÷2516-4914)Answer:13Explanation:Simplify and add (if possible).15)212+ 42715)Answer:163Explanation:Simplify using the quotient property of exponents. Write the answer using positive exponents only.16)7m-1016)Answer:7m10Explanation:Simplify the expression. Assume the variable represents a nonnegative real number.17)45n217)Answer:3n5Explanation:Perform the operation indicated. Write final result in lowest terms.18)112s-98s218)Answer:44s-98s2Explanation:List all the numbers in the set that are elements of W.19)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3619)Answer:{36}Explanation:Translate the phrase into an algebraic expression.20)the difference between a number andsixis squared20)Answer:(n–6)2Explanation:3

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Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” ifneeded) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.”21)x3-4x2-9x+3621)Answer:(x-4)(x+3)(x-3)Explanation:List all the numbers in the set that are elements of R.22)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3622)Answer:-3.5, -134, 3.25, -3, -0.8,ʌ,92,36Explanation:Reduce to lowest terms.23)b- 5-2b+ 1023)Answer:-12Explanation:Rewrite the expression as a compound fraction. Then simplify using either method.24)1 +6x-11 -6x-124)Answer:1 +6x1 -6x;x+6x-6Explanation:Factor by grouping.25)Factor by grouping.x5+ 2x3- 4x2- 825)Answer:(x2+ 2)(x3- 4)Explanation:Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” ifneeded) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.”26)-21x2+ 6x+ 15x326)Answer:3x(5x- 2)(x- 1)Explanation:4

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Simplify using the quotient property of exponents. Write the answer using positive exponents only.27)-16w24-4w827)Answer:4w16Explanation:Create a mathematical model using descriptive variables.28)The speed of the truck wastwomiles per hour more than the speed of the car.28)Answer:Letcrepresent the speed of the car. Thenc+2represents2mphmore thanthe speed of the car.Explanation:Simplify by combining like terms.29)-2b- 9b- 6b29)Answer:-17bExplanation:Simplify the expression by building a perfect square root factor for the denominator.30)362230)Answer:182211Explanation:List all the numbers in the set that are elements of N.31)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3631)Answer:{36}Explanation:Use the properties of exponents to simplify the expression. Write the answer using positive exponentsonly.32)3m2n56mn532)Answer:m2Explanation:5

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Evaluate the expression for the given value(s).33)2x2ygivenx=-3andy=5.33)Answer:90Explanation:34)3x- 5ygivenx=2andy=-2.34)Answer:16Explanation:Simplify by removing all grouping symbols and combining like terms.35)10a+ (-3a)35)Answer:7aExplanation:Convert to decimal form and graph by estimating the number's location between two integers.36)8336)Answer:2.6Explanation:Compute the product and simplify the result.37)(8+5)(8-5)37)Answer:59Explanation:Evaluate the expression for the given value(s).38)8Â-20ygiveny= -5.38)Answer:80Explanation:Convert the following number to decimal notation.39)The maximum distance from Pluto to the Sun is7.3 ×1012meters.39)Answer:7,300,000,000,000 metersExplanation:6

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Perform the operation indicated. Write final result in lowest terms.40)1x+ 1+xx2- 4x- 540)Answer:2x- 5(x- 5)(x+ 1)Explanation:Perform the operation indicated without the aid of a calculator.41)37÷ (-12)41)Answer:-128Explanation:Simplify the expression, assuming that the variable can represent any real number.42)3p32742)Answer:p3Explanation:Rewrite the expression using the commutative property of addition and simplify if possible.43)-3+143)Answer:1+ (-3) =-2Explanation:Write the polynomial in standard form and name the lead coefficient.44)9x2+ 5x3- 1+ (-3x)44)Answer:5x3+ 9x2- 3x- 1;5Explanation:7

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The costC, in millions of dollars, for a government to find and seizeP% of an illegal drug is modeled bythe rational equationC=350P100 -P(0P< 100).45)Complete the table. Round to the nearest dollar.P350P100 -P4060809092959710045)Answer:P350P100 -P40233605258014009031509240259566509711317100ERRORExplanation:Find the binomial square.46)(x+ 6)246)Answer:x2+ 12x+ 36Explanation:Evaluate/Simplify the expression.47)|-6.8|47)Answer:6.8Explanation:Factor the trinomial completely.48)x2- 5x- 1448)Answer:(x+ 2)(x- 7)Explanation:8

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Identify the number of terms in the expression and the coefficient of each term.49)-5x2+x-949)Answer:three terms; coefficients:-5, 1,-9Explanation:Simplify the expression. Write your answer using positive exponents only.50)-20a8b310a4b-250)Answer:-2a4b5Explanation:Solve the problem.51)For the binomial7x- 5a. Determine its conjugate.b. Find the product of the binomial with its conjugate.51)Answer:a.7x+ 5b.49x2- 25Explanation:Factor the difference of perfect squares completely.52)49x2- 952)Answer:(7x+ 3)(7x- 3)Explanation:MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Simplify the expression.53)-6453)A)-8B)8C)-32D)not a real numberAnswer:DExplanation:A)B)C)D)54)18+63354)A)6+21B)6+37C)6+7D)6+63Answer:CExplanation:A)B)C)D)9

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Find the binomial square.55)(3x- 7)255)A)3x2- 21x+ 49B)9x2+ 49C)9x2- 42x+ 49D)9x2- 21x+ 49Answer:CExplanation:A)B)C)D)Evaluate the expression for the given value(s).56)3y2+ 4y- 5 giveny=-2.56)A)-1B)15C)-9D)-25Answer:AExplanation:A)B)C)D)Perform the operation indicated. Write final result in lowest terms.57)x2+ 2x- 3x2- 3x- 10÷x2- 9x2- 25Âx- 3x- 157)A)x+ 2x+ 5B)(x+ 5)(x- 1)2(x+ 2)(x- 3)2C)(x+ 2)(x- 3)2(x+ 5)(x- 1)2D)x+ 5x+ 2Answer:DExplanation:A)B)C)D)Perform the operation indicated without the aid of a calculator.58)-6- (-44)58)A)-50B)-38C)38D)50Answer:CExplanation:A)B)C)D)10

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Translate the key phrase into an algebraic expression. Use descriptive variables.59)The length of a rectangular lawn is6ftless thanthreetimes the width of the lawn.Express the length of the lawn in terms of the width.59)A)3w-6B)3+w-6C)6w-3D)3(w-6)Answer:AExplanation:A)B)C)D)Perform the operation indicated. Write final result in lowest terms.60)a+ 3a2- 4-a+ 5a2- 4a+ 460)A)-6a+ 4(a+ 2)2(a- 2)B)-6a- 16(a+ 2)2(a- 2)C)-6a+ 4(a+ 2)(a- 2)2D)-6a- 16(a+ 2)(a- 2)2Answer:DExplanation:A)B)C)D)Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” ifneeded) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.”61)x2+ 2x+ 361)A)(x+ 2)(x+ 1)B)(x+ 3)(x+ 1)C)(x– 3)(x– 1)D)primeAnswer:DExplanation:A)B)C)D)Simplify the expression using the product to a power property.62)(-2ab10)262)A)4a2b20B)-4ab20C)-4a2b20D)4ab20Answer:AExplanation:A)B)C)D)11

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Evaluate/Simplify the expression.63)1663)A)-6B)-16C)6D)16Answer:DExplanation:A)B)C)D)Simplify the expression.64)-943264)A)278B)272C)-278D)not a real numberAnswer:DExplanation:A)B)C)D)Use the properties of exponents to simplify the expression. Write the answer using positive exponentsonly.65)-7x0+(-7x)065)A)-14B)-2C)-6D)0Answer:CExplanation:A)B)C)D)Factor the difference of perfect cubes completely.66)27a3- 100066)A)(3a+ 10)(9a2- 30a+ 100)B)(3a- 10)(9a2+ 30a+ 100)C)(3a+ 10)(9a2- 100)D)(3a- 10)(9a2+ 100)Answer:BExplanation:A)B)C)D)12

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The costC, in millions of dollars, for a government to find and seizeP% of an illegal drug is modeled bythe rational equationC=350P100 -P(0P< 100).67)What is the cost of seizing 60% of the drugs?67)A)$525B)$350C)$210D)$233Answer:AExplanation:A)B)C)D)List all the numbers in the set that are elements of H.68)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3668)A)-134, -3,ʌ,92,36B)-3,ʌ,36C)-3,ʌD)-134, -3,ʌ,92Answer:CExplanation:A)B)C)D)Compute the product.69)(3x- 1)(2x +5)69)A)6x2+ 13x- 5B)6x2+ 17x- 5C)6x2- 13x- 5D)6x2- 17x- 5Answer:AExplanation:A)B)C)D)Use a descriptive variable and an inequality symbol(<, >,,)to write a model for the statement.70)TheEllisfamily will spendat least$9500on home improvements.70)A)Letarepresent the amount.a$9500.B)Letarepresent the amount.a$9500.C)Letarepresent the amount.a<$9500.D)Letarepresent the amount.a>$9500.Answer:AExplanation:A)B)C)D)13

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Factor each expression completely, if possible. Rewrite the expression in standard form (factor out “-1” ifneeded) and factor out the GCF if one exists. If you believe the expression will not factor, write “prime.”71)x2- 14x+ 4071)A)(x- 4)(x+ 10)B)(x+ 1)(x+ 40)C)(x- 4)(x- 10)D)(x+ 4)(x+ 10)Answer:CExplanation:A)B)C)D)Simplify the expression using the quotient to a power property.72)2y9z7272)A)4y18z7B)2y11z9C)4y18z14D)4y11z7Answer:CExplanation:A)B)C)D)Reorder the elements of the set in order from smallest to largest.73)-3.5, -134, 3.25, -3, -0.8,ʌ,92,3673)A)-3.5, -134, -3, -0.8,ʌ, 3.25,92,36B)-3.5, -134, -3, -0.8, 3.25,ʌ,92,36C)-3.5, -3, -134, -0.8, 3.25,ʌ,92,36D)-3.5, -3, -134, -0.8,ʌ, 3.25,92,36Answer:AExplanation:A)B)C)D)14

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Perform the operation indicated. Write final result in lowest terms.74)n2-n- 20n2+ 8n+ 16Ânn2- 2574)A)n(n+ 5)(n+ 4)B)n(n+ 4)(n+ 5)C)n(n+ 4)(n- 5)D)n(n+ 5)(n+ 4)2Answer:BExplanation:A)B)C)D)Convert the following number to scientific notation.75)The diameter of Jupiter is approximately 143,000,000 meters.75)A)1.43 ×107metersB)1.43 ×108metersC)14.3 ×108metersD)14.3 ×107metersAnswer:BExplanation:A)B)C)D)Simplify by combining like terms.76)4x+ 14x2- 9x- 5x276)A)9x2+ 5xB)-9x2- 5xC)9x2- 5xD)18x2- 14xAnswer:CExplanation:A)B)C)D)Factor the trinomial completely.77)6x2- 5x- 677)A)(2x+ 3)(3x- 2)B)(2x+ 1)(3x- 6C)(2x- 3)(3x+ 2)D)(6x- 3)(x+ 2)Answer:CExplanation:A)B)C)D)15

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