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    Ch. 0 Chapter P: Prerequisites: Fundamental Concepts of Algebra 0.1 Algebraic Expressions, Mathematical Models, and Real Numbers 1 Evaluate Algebraic Expressions MULTIPLE 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) 9x + 8; x = 7 A) 71 B) 126 C) 17 D) 55 2) 8x + 3; x = - 2 A) - 13 B) 19 C) - 19 D) 13 3) 2(x + 1) + 21; x = - 4 A) 15 B) - 15 C) 35 D) 7 4) 6x 2 + 8y; x = 7 and y = 5 A) 334 B) 1804 C) 1710 D) 206 5) (x + 4y)2; x = 4 and y = 2 A) 144 B) 12 C) 24 D) 64 6) 2 + 6(x - 6) 3 ; x = 8 A) 50 B) 14 C) 64 D) - 46 7) x 2 - 4(x - y); x = 6 and y = 2 A) 20 B) 10 C) 14 D) - 52 8) 6(x + 3) 2x + 2 ; x = 5 A) 4 B) 1 C) 8 D) 11 2 9) y - 4x 7x + xy ; x = - 1 and y = 3 A) - 7 10 B) 1 10 C) 1 4 D) - 9 10 2 Use Mathematical Models MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. 1) The formula C = 5 9 (F - 32) expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. Use the formula to convert 68°F to its equivalent temperature on the Celsius scale. A) 20°C B) 4°C C) 56°C D) 65°C Page 1

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    2) A stone is dropped from a tower that is 770 feet high. The formula h = 770 - 16t 2 describes the stone's height above the ground, h, in feet, t seconds after it was dropped. What is the stone's height 4 seconds after it is released? A) 514 ft B) 524 ft C) 489 ft D) 539 ft 3) If a rock falls from a height of 50 meters above the ground, the height H (in meters) after x seconds can be approximated using the formula H = 50 - 4.9x 2 . What is the height of the rock after 3 seconds? A) 5.9 m B) 405.9 m C) - 166.09 m D) 35.3 m 4) As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.113x + 77.98 approximates the apparent temperature for an actual temperature of 85°F, where x is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of 40%? A) 83°F B) 352°F C) 118°F D) 78°F 5) The winning times (in seconds) in a speed - skating event for men can be represented by the formula T = 46.18 - 0.095x, where x represents the year, with x = 0 corresponding to 1920. (For example in 1992, x would be 1992 - 1920 = 72.) According to the formula, what was the winning time in 1998? Round to the nearest hundredth. A) 38.77 sec B) 3594.63 sec C) 39.72 sec D) 40.67 sec 6) It is estimated that y, the number of items of a particular commodity (in millions) sold in the United States in year x, where x represents the number of years since 1990, is given by the formula y = 1.3x + 3.07. That is, x = 0 represents 1990, x = 1 represents 1991, and so on. According to the formula, how many items sold in 1995? A) 9.57 millions B) 3.07 millions C) 21.85 millions D) 10.87 millions 3 Find the Intersection of Two Sets MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the intersection of the two sets. 1) {1, 3, 5, 8} ∩ {5, 11, 1} A) {1, 5} B) {1} C) {1, 5, 8, 3, 11} D) ∅ 2) {2, 10, 8} ∩ {4, 6} A) ∅ B) {10, 8} C) {2, 4, 8, 10, 6} D) {2, 8} 3) {6, 8, 9, 11} ∩ ∅ A) ∅ B) {6, 8, 9, 11} C) {6, 8} D) {9, 11} 4 Find the Union of Two Sets MULTIPLE 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, 10} ∪ {2, 5, 12} A) {2, 5, 8, 10, 12} B) {2, 5} C) {8, 10, 12} D) ∅ 2) {2, 10} ∪ {2, 4, 8} A) {2, 4, 8, 10} B) {2} C) {4, 8, 10} D) ∅ 3) {1, 3, 4, 6} ∪ ∅ A) {1, 3, 4, 6} B) {1, 3} C) {4, 6} D) ∅ Page 2

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    5 Recognize Subsets of the Real Numbers MULTIPLE 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 = {17, 5, - 22, 0, 0.6, 25} Integers A) 17, - 22, 0, 25 B) 17, 0 C) 17, - 22, 0 D) 17, 0, 25 2) B = {11, 6, - 16, 0, 0.1, 4} Whole numbers A) 11, 0, 4 B) 11, - 16, 0 C) 11, - 16, 0, 4 D) 11, 0 3) B = {10, 6, - 9, 0, 0.6, 9} Natural numbers A) 10, 9 B) 10, 0, 9 C) 10, 0 D) 10 4) B = {16, 5, - 2, 0, 8 9 , 25, 0.3, 0.73} Rational numbers A) 16, - 2, 0, 8 9 , 25, 0.73, 0.3 B) 16, 0, 25 C) 5, 25 D) 5, 8 9 , 0.73 5) B = {11, 7, - 11, 0, 5 6 , 4, 0.7, 0.35} Irrational numbers A) 7 B) 7, 0.7 C) 7, 4, 0.7 D) 7, 4, 0.35 6) B = {4, 8, 0, 5 6 , 9, - 0.9, 0.53, - 23} Real numbers A) 4, 8, 0, 5 6 , 9, - 0.9, 0.53, - 23 B) 4, 8, 0, 5 6 , 9, 0.53 C) 4, 8, 5 6 , 9, - 0.9, 0.53, - 23 D) 4, 0, 5 6 , - 0.9, 0.53, - 23 6 Use Inequality Symbols MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 1) 21 > 24 A) False B) True 2) 17 ≥ 4 A) True B) False 3) - 81 < 0 A) True B) False 4) 24 < - 6 A) False B) True 5) 12 ≤ 11 A) False B) True Page 3

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    6) - 5 ≤ 8 A) True B) False 7) 15 > 13 A) True B) False 8) - 8 ≥ 15 A) False B) True 9) - π ≥ - π A) True B) False 10) π < 3 A) False B) True 7 Evaluate Absolute Value MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Rewrite the expression without absolute value bars. 1) |13| A) 13 B) - 13 C) 26 D) 0 2) | - 2| A) 2 B) - 2 C) 4 D) 0 3) 19 - 1 A) 19 B) - 1 C) 1 D) - 19 4) 10 - 13 A) 13 - 10 B) 10 - 13 C) - 3 D) 3 5) |5 + ( - 10)| A) 5 B) 15 C) - 5 D) - 15 6) - 4 - - 9 A) 5 B) 13 C) - 5 D) - 13 7) - 6 + - 8 A) 14 B) 2 C) - 2 D) - 14 Evaluate the expression for the given values of x and y. 8) |x| x + |y| y ; x = 6 and y = - 3 A) 0 B) 2 C) 1 D) - 1 Page 4

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    8 Use Absolute Value to Express Distance MULTIPLE 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 the absolute value expression. 1) 26 and 34 A) |26 - 34| = 8 B) - |34 - 26| = - 8 C) |26 + 34| = 60 D) - |26 + 34| = - 60 2) - 18 and - 34 A) |( - 18) - ( - 34)| = 16 B) |( - 34) - ( - 18)| = - 16 C) |( - 34) + ( - 18)| = - 52 D) | - ( - 18) + ( - 34)| = 52 3) 72 and - 9 A) |72 - ( - 9)| = 81 B) |( - 9) - 72| = - 81 C) |72 + ( - 9)| = 63 D) | - 72 + ( - 9)| = - 63 4) 28.9 and 23.7 A) |28.9 - 23.7| = 5.2 B) |23.7 - 28.9| = - 5.2 C) |28.9 + 23.7| = 52.6 D) | - 28.9 + 23.7| = - 52.6 5) - 14.7 and 24.3 A) | - 14.7 - 24.3| = 39.0 B) |24.3 + ( - 14.7)| = - 39.0 C) |24.3 - ( - 14.7)| = 9.6 D) | - 14.7 + ( - 24.3)| = - 9.6 6) 1.5 and 48.3 A) |1.5 - 48.3| = 46.8 B) |48.3 - 1.5| = - 46.8 C) |48.3 + 1.5| = 49.8 D) - |1.5 + 48.3| = - 49.8 9 Identify Properties of the Real Numbers MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. State the name of the property illustrated. 1) 6 + ( - 7) = ( - 7) + 6 A) Commutative property of addition B) Associative property of addition C) Distributive property of multiplication over addition D) Identity property of addition 2) 17 · (6 + 8) = 17 · 6 + 17 · 8 A) Distributive property of multiplication over addition B) Commutative property of multiplication C) Associative property of multiplication D) Commutative property of addition 3) 2 + (8 + 7) = (2 + 8) + 7 A) Associative property of addition B) Commutative property of addition C) Distributive property of multiplication over addition D) Identity property of addition Page 5

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    4) (7 + 3) + 4 = (3 + 7) + 4 A) Commutative property of addition B) Associative property of addition C) Distributive property of multiplication over addition D) Inverse property of addition 5) 5 · (6 · 17) = 5 · (17 · 6) A) Commutative property of multiplication B) Associative property of multiplication C) Distributive property of multiplication over addition D) Identity property of multiplication 6) (9 + 6) + (7 + 19) = (7 + 19) + (9 + 6) A) Commutative property of addition B) Associative property of addition C) Distributive property of multiplication over addition D) Inverse property of addition 7) 3 · (19 · 2) = (19 · 2) · 3 A) Commutative property of multiplication B) Associative property of multiplication C) Distributive property of multiplication over addition D) Identity property of multiplication 8) (8 · 12) · 7 = 8 · (12 · 7) A) Associative property of multiplication B) Commutative property of multiplication C) Distributive property of multiplication over addition D) Identity property of multiplication 9) 7(x + 6) = 7x + 7 · 6 A) Distributive property of multiplication over addition B) Commutative property of multiplication C) Associative property of multiplication D) Identity property of multiplication 10) 3( - 5 + 7) = - 15 + 21 A) Distributive property of multiplication over addition B) Associative property of multiplication C) Associative property of addition D) Commutative property of multiplication 11) - 7(6 + 7) = - 42 + ( - 49) A) Distributive property of multiplication over addition B) Associative property of multiplication C) Associative property of addition D) Commutative property of multiplication 12) 1 (x + 2) (x + 2) = 1, x ≠ - 2 A) Inverse property of multiplication B) Inverse property of addition C) Commutative property of multiplication D) Identity property of multiplication Page 6

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    13) (x + 3) + [ - (x + 3)] = 0 A) Inverse property of addition B) Inverse property of multiplication C) Commutative property of addition D) Identity property of multiplication 10 Simplify Algebraic Expressions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the algebraic expression. 1) - 8(6r + 3) + 4(9r + 4) A) - 12r - 8 B) - 2r - 5 C) - 12r + 3 D) - 72r 2) (11z + 6) - (4z - 4) A) 7z + 10 B) 7z + 2 C) 15z + 10 D) 7z - 10 3) - 6(2x - 9) - 4x + 5 A) - 16x + 59 B) 8x + 59 C) 16x + 59 D) - 16x - 49 Write the algebraic expression without parentheses. 4) - (49x) A) - 49x B) 49x C) - 49 - x D) 49 - x 5) - 8( - 8z) A) 64z B) - 64z C) 64 - 8z D) 64 + z 6) - (3x - 9) A) - 3x + 9 B) 3x - 9 C) - 3x - 9 D) 27x 7) - ( - 9 + 5y) A) 9 - 5y B) 9 + 5y C) - 9 + 5y D) 45y 8) - (7z - 2w + 6y) A) - 7z + 2w - 6y B) - 7z + 2w + 6y C) - 7z - 2w + 6y D) - 7z - 2w - 6y 9) 1 5 (5x) + [(4x) + ( - 4x)] A) x B) 9x C) - 7x D) 1 0.2 Exponents and Scientific Notation 1 Use the Product Rule MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) 83 · 88 A) 811 B) 824 C) 6411 D) 6424 2) y · y 11 A) y 12 B) 2y 11 C) y 11 D) 2y 12 3) x 8 · x 9 A) x 17 B) x 72 C) 17x D) 72x Page 7

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    4) (3x4)(9x9) A) 27x 13 B) - 27x 13 C) 27x 36 D) - 27x 36 5) ( - 8x 5 y)( - 3x 3 y 6 ) A) 24x 8 y 7 B) - 24x 8 y 6 C) - 11x 8 y 6 D) 24x 15 y 6 2 Use the Quotient Rule MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) 5 5 5 6 A) 1 5 B) 5 C) - 12,500 D) 5 6 2) x 14 x 10 A) x 4 B) x 24 C) x 8 D) 1 x 4 3) x 2 x 6 A) 1 x 4 B) - x 4 C) x 4 D) - 1 x 4 4) 6x 10 x 7 A) 6x 3 B) 216x 3 C) 6x 17 D) 18x 5) - 30x 11 5x 8 A) - 6x 3 B) x 2 C) x 3 D) - 6x 2 6) x 13 y 13 x 2 y 2 A) x 11 y 11 B) x 10 y 10 C) xy 11 D) x 10 y 11 7) - 32x 12 y 11 8x 8 y 3 A) - 4x 4 y 8 B) x 4 y 8 C) - 4x 3 y 4 D) - 4x 3 y 7 Page 8

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    8) - 27x 7 3x 10 A) - 9 x 3 B) - 9x 3 C) - 9 x 2 D) - 9x 2 9) - 10x 13 y 12 z 6 5x 7 y 3 z 5 A) - 2x 6 y 9 z B) x 6 y 9 z C) - 2x 5 y 8 z D) - 2x 6 y 9 3 Use the Zero - Exponent Rule MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) 4 0 A) 1 B) - 1 C) 0 D) 4 2) ( - 2) 0 A) 1 B) - 1 C) 0 D) 2 3) - 6 0 A) - 1 B) 1 C) 0 D) 6 4) x 6 y 0 A) x 6 B) 1 C) 0 D) 1 x 6 5) - 7y 0 A) - 7 B) 1 C) 0 D) - 6 6) (7b) 0 A) 1 B) 0 C) b D) 7 7) - 72x 9 y 13 8x 3 y 4 0 A) 1 B) x 6 y 9 C) - 9x 6 y 9 D) 0 4 Use the Negative - Exponent Rule MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) 3 - 4 A) 1 81 B) - 81 C) 81 D) 1 12 2) ( - 3) - 2 A) 1 9 B) - 9 C) 9 D) - 1 9 Page 9

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    3) - 4 - 3 A) - 1 64 B) - 64 C) 64 D) 1 12 4) 3 - 3 · 3 A) 1 9 B) 1 27 C) 9 D) 27 5) 3 3 · 3 - 4 A) 1 3 B) - 3 C) 2187 D) - 1 3 6) x 7 · x - 2 A) x 5 B) 1 x 5 C) - x 5 D) - 1 x 5 7) x - 9 · x 7 A) 1 x 2 B) - x 2 C) x 2 D) - 1 x 2 8) x 2 y - 3 A) x 2 y 3 B) y 3 x 2 C) x 2 y 15 D) y 15 x 2 9) 8x - 8 y 2 A) 8y 2 x 8 B) 8 x 8 y 2 C) y 2 8x 8 D) 8x 8 y 2 10) x - 6 x4 A) 1 x10 B) 1 x24 C) 1 x2 D) x10 11) x - 3 y - 2 A) y 2 x 3 B) 1 x 3 y 2 C) x 3 y 2 D) x 3 y 2 12) x 8 y - 3 z - 8 A) x 8 z 8 y 3 B) z 8 x 8 y 3 C) y 3 x 8 z 8 D) x 8 z 3 y 8 Page 10

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    13) 10x 3 y 14 5x 2 y - 10 A) 2xy 24 B) 10xy 24 C) 2x 5 y 24 D) 2xy 4 5 Use the Power Rule MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) (3 4 ) 2 A) 6561 B) 729 C) 24 D) 162 2) (4 3 ) - 2 A) 1 4096 B) 1 1024 C) - 24 D) - 128 3) (x 7 ) 8 A) x 56 B) x 15 C) 8x 7 D) 8x 56 4) (x - 6 ) 4 A) 1 x 24 B) - x 24 C) - 6x 4 D) - 6x 24 5) (x 9 ) - 6 A) 1 x 54 B) - x 54 C) - 6x 9 D) - 6x 54 6) (x - 4 ) - 3 A) x 12 B) 1 x 12 C) 1 x 7 D) - x 7 6 Find the Power of a Product MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) (5x)3 A) 125x3 B) 15x C) 125x D) 15x3 2) ( - 2x)5 A) - 32x5 B) - 10x C) - 32x D) - 10x5 3) (6x 3 ) 2 A) 36x 6 B) 6x 6 C) 36x 3 D) 6x 5 4) (x 7 y) 4 A) x 28 y 4 B) x 28 y C) x 11 y 5 D) x 11 y Page 11

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    5) ( - 6x 4 y 5 ) 2 A) 36x 8 y 10 B) - 6x 8 y 10 C) - 36x 8 y 10 D) 36x 6 y 7 6) (4x 3 ) - 2 A) 1 16x 6 B) 1 4x 6 C) 16x 6 D) 16 x 6 7) (x - 1y4) - 2 A) x2 y8 B) x - 3 y2 C) 1 x2y8 D) y2 x - 3 8) (3x - 6 y 2 z - 5 ) - 3 A) x 18 z 15 27y 6 B) y 5 27x 9 z 8 C) x 18 z 15 - 9y - 6 D) y 5 - 9x 9 z 8 7 Find the Power of a Quotient MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the exponential expression. 1) x 6 3 A) x 3 216 B) x 4 1296 C) x 6 D) x 3 6 2) - 5 x 3 A) - 125 x 3 B) 125 x 3 C) - 125 x D) - 5 x 3 3) x4 2 2 A) x8 4 B) x8 2 C) x6 4 D) x6 2 4) - 3x y 2 A) 9x 2 y 2 B) 9x y 2 C) - 6x 2 y 2 D) - 6x y 5) 3x4y2 z2 3 A) 27x12y6 z6 B) 3x12y6 z6 C) 27x7y5 z5 D) 3x12y6 z5 Page 12

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    6) - 21x 12 y 6 7x 17 y - 2 3 A) - 27y 24 x 15 B) 27y 24 x 15 C) - 27y 12 x 15 D) - 27 x 15 y 24 7) x - 1 y 5 - 3 A) x 3 y 15 B) x - 4 y 2 C) 1 x 3 y 15 D) y 2 x - 4 8) 2x 3 y 2 - 3 A) y 6 8x 9 B) 8x 9 y 6 C) 8y 6 x 9 D) y 2 8x 9 8 Simplify Exponential Expressions MULTIPLE 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) 3 3 · 5 A) 135 B) 45 C) 3375 D) 32 2) ( - 5) 3 A) - 125 B) 125 C) - 15 D) 15 3) - 63 A) - 216 B) 18 C) 216 D) - 18 4) (3x 3 ) 3 x 15 A) 27 x 6 B) 3 x 6 C) 27 x 9 D) 27 x 24 5) ( - 5x 4 y - 5 )(3x - 1 y) A) - 15x 3 y 4 B) - 15x 3 y 6 C) - 2x 3 y 4 D) - 15x 5 y 6 6) 5 - 9 x - 2 y 3 5 - 6 x - 5 y 6 A) x 3 125y 3 B) 1 125x 5 y 3 C) 3x 3 y 3 D) 125 x 3 y 3 Page 13

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    7) xy 6 x 6 y - 2 A) x 10 y 10 B) 1 x 8 y 13 C) 1 x 14 y 14 D) y 10 x 10 8) 6x - 4 y - 2 z 3 2xy - 2 z - 3 - 1 A) x 5 3z 6 B) x 3 3z 6 C) 3x 5 z 6 D) x 5 y 4 3z 6 9 Use Scientific Notation MULTIPLE 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) 4 × 10 - 4 A) 0.0004 B) 40,000 C) 0.004 D) 4000 2) 2 × 10 5 A) 200,000 B) 0.00002 C) 2,000,000 D) 0.000002 3) 5.01 × 107 A) 50,100,000 B) 501,000,000 C) 5,010,000 D) 350.7 4) 4.14 × 10 - 4 A) 0.000414 B) 0.00414 C) 0.0000414 D) - 414,000 5) 5.201 × 10 - 6 A) 0.000005201 B) 0.00005201 C) 0.0000005201 D) - 5,201,000 6) - 6.77 × 104 A) - 67,700 B) - 677,000 C) - 6770 D) 67,700 7) - 1.0077 × 10 4 A) - 10,077 B) - 100,770 C) - 1007.7 D) - 40.308 Write the number in scientific notation. 8) 2,012,310 A) 2.01231 × 106 B) 2.01231 × 107 C) 2.01231 × 10 - 6 D) 2.01231 × 101 9) 24,000 A) 2.4 × 10 4 B) 2.4 × 10 - 4 C) 2.4 × 10 3 D) 2.4 × 10 - 3 10) 57,000,000 A) 5.7 × 107 B) 5.7 × 10 - 7 C) 5.7 × 108 D) 5.7 × 10 - 8 11) 472 A) 4.72 × 102 B) 4.72 × 103 C) 4.72 × 10 - 2 D) 4.72 × 101 Page 14

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    12) 0.000585 A) 5.85 × 10 - 4 B) 5.85 × 10 4 C) 5.85 × 10 - 5 D) 5.85 × 10 - 3 13) 0.000048919 A) 4.8919 × 10 - 5 B) 4.8919 × 105 C) 4.8919 × 10 - 4 D) 4.8919 × 104 14) 0.000000088007 A) 8.8007 × 10 - 8 B) 8.8007 × 10 8 C) 8.8007 × 10 - 7 D) 8.8007 × 10 - 9 Perform the indicated computation. Write the answer in scientific notation. 15) (5 × 10 - 9 )(7 × 10 - 4 ) A) 3.5 × 10 - 12 B) 35 × 10 - 12 C) 350 × 10 - 13 D) 3.5 × 10 36 16) (2 × 10 - 4 )(3.2 × 10 - 7 ) A) 6.4 × 10 - 11 B) 6.4 × 10 - 10 C) 64 × 10 - 11 D) 6.4 × 10 28 17) 8 × 10 2 4 × 10 3 A) 2 × 10 - 1 B) 2 × 10 5 C) 4 × 10 - 1 D) 4 × 10 5 18) 17.15 × 10 - 6 5 × 10 - 3 A) 3.43 × 10 - 3 B) 3.43 × 10 - 9 C) 6.86 × 10 - 3 D) 6.86 × 10 - 9 19) 5.52 × 10 1 2.4 × 10 - 8 A) 2.3 × 10 9 B) 2.3 × 10 - 7 C) 4.6 × 10 9 D) 4.6 × 10 - 7 20) 30,000,000,000 0.00006 A) 5 × 10 14 B) 5 × 10 13 C) 24 × 10 14 D) 24 × 10 13 21) 0.00018 × 0.0003 0.0009 A) 6 × 10 - 5 B) 6 × 10 5 C) 54 × 10 6 D) 54 × 10 - 6 Solve. Express the result in scientific notation. If necessary, round the decimal factor to two decimal places. 22) In a state with a population of 5,000,000 people, the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state? A) $3 × 10 10 B) $3 × 10 9 C) $30 × 10 11 D) $30 × 10 10 23) Approximately 8 × 10 3 employees of a certain company average $30,000 each year in salary. What is the total amount earned by all the employees of this company per year? A) $2.4 × 10 8 B) $24 × 10 8 C) $2.4 × 10 9 D) $24 × 10 9 Page 15

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    0.3 Radicals and Rational Exponents 1 Evaluate Square Roots 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) 16 A) 4 B) 256 C) 1 16 D) Not a real number 2) - 625 A) - 25 B) 25 C) - 312 D) Not a real number 3) - 144 A) 12 144 B) 20,736 C) 12 D) Not a real number 4) 16 + 9 A) 5 B) 7 C) 25 D) 7 5) 25 - 9 A) 4 B) 7 C) 16 D) 7 6) 64 + 36 A) 14 B) 10 C) 100 D) 28 2 Simplify 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) (7) 2 A) 7 B) 2401 C) 1 49 D) Not a real number 2) ( - 5) 2 A) 5 B) 25 C) - 5 D) Not a real number 3 Use the Product Rule to Simplify Square Roots MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the product rule to simplify the expression. 1) 96 A) 4 6 B) 6 4 C) 24 D) 9 2) 15 A) 15 B) 5 3 C) 3 5 D) 3 3) 175 A) 5 7 B) 175 C) 35 D) 25 7 Page 16

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    4) 192x 2 A) 8 x 3 B) 8 3x C) 192x D) 3x 2 8 5) 448x 2 A) 8 x 7 B) 8 7x 2 C) 8x 2 7 D) 8 7 6) 14x · 28x A) 14 x 2 B) 14 2x C) 14x 2 2 D) 14 2x 2 7) 7x 2 · 21x A) 7 x 3x B) 7 x 3 C) 7x 2 3x D) 7 x 3x 2 Solve the problem. 8) Racing cyclists use the algebraic expression 4 x to determine the maximum speed, in miles per hour, to turn a corner of radius x, in feet, without tipping over. Find the maximum speed at which a cyclist should travel around a corner of radius 38 feet without tipping over. Write the answer in simplified radical form. A) 4 38 miles per hour B) 24 2 miles per hour C) 24 + 2 miles per hour D) 4(6 + 2) x miles per hour 9) The formula v = 2.5r models the safe maximum speed, v, in miles per hour, at which a car can travel on a curved road with radius of curvature, r, in feet. A highway crew measures the radius of curvature at an exit ramp as 490 feet. What is the maximum safe speed? A) 35 miles per hour B) 49 miles per hour C) 40 miles per hour D) 32 miles per hour 10) 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 accident and its skid marks measure 245 feet, at what estimated speed was the car traveling when it applied its brakes just prior to the accident? A) 70 miles per hour B) 75 miles per hour C) 65 miles per hour D) 80 miles per hour 11) The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 36 months of age and a child 25 months of age? A) 2.9 inches B) 43.1 inches C) 17.4 inches D) 4.9 inches 4 Use the Quotient Rule to Simplify Square Roots MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the quotient rule to simplify the expression. 1) 1 4 A) 1 2 B) 1 16 C) 2 D) 4 Page 17

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    2) 64 25 A) 8 5 B) 1 C) 8 5 D) 8 5 3) 32x 3 2x A) 4 x B) 4 x 2 C) 2x 2 D) 4x 2 2 4) 100x 4 5x A) 2 x 5x B) 100x 3 C) 5 x x D) x 2 100 5 Solve the problem. 5) The time, in seconds, that it takes an object to fall a distance d, in feet, is given by the algebraic expression d 16 . Find how long it will take a ball dropped from the top of a building 83 feet tall to hit the ground. Write the answer in simplified radical form. A) 83 4 seconds B) 9 2 4 seconds C) 83 16 seconds D) 9 + 2 4 seconds 5 Add and Subtract Square Roots MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract terms whenever possible. 1) 6 3 + 2 3 A) 8 3 B) 12 6 C) 8 6 D) 4 3 2) 7 6 + 5 54 A) 22 6 B) 8 6 C) 12 6 D) - 22 6 3) 8 3x + 3 3x A) 11 3x B) 24 6x C) 11x 6 D) 5 3 4) 3 3 + 9 12 A) 21 3 B) 15 3 C) 12 3 D) - 21 3 5) - 6 162 + 2 128 + 7 98 A) 11 2 B) - 6 2 C) 66 2 D) - 66 2 6) 16 + 245 + 4 + 405 A) 16 5 + 6 B) 16 5 + 16 + 4 C) 245 + 405 + 6 D) 130 5 + 6 7) 5x - 5 45x + 2 80x A) - 6 5x B) - 6 130x C) - 3 130x D) - 3 5x Page 18

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    6 Rationalize Denominators MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Rationalize the denominator. 1) 1 17 A) 17 17 B) 17 C) 1 + 17 D) 1 + 17 17 2) 10 10 A) 10 B) 10 10 C) 10 D) 1 3) 144 11 A) 12 11 11 B) 12 11 C) 144 11 11 D) 133 4) 144 11 A) 12 11 11 B) 12 11 C) 144 11 11 D) 133 5) 3 7 A) 21 7 B) 21 49 C) 21 D) 3 6) 5 8 - 10 A) 40 + 5 10 54 B) 40 - 5 10 54 C) 40 + 5 10 2 D) 5 8 - 5 10 7) 6 17 + 2 A) 102 - 2 6 13 B) 102 + 2 6 13 C) 102 - 2 6 19 D) 3 102 + 17 34 6 8) 3 4 - 2 A) 12 + 3 2 14 B) 12 - 3 2 14 C) 12 + 3 2 2 D) 3 4 - 3 2 9) 5 6 + 11 A) 11 - 6 B) 6 - 11 C) 11 + 6 D) 5 Page 19

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    7 Evaluate and Perform Operations with Higher Roots MULTIPLE 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 64 A) 4 B) - 4 C) 64 D) not a real number 2) 3 ( - 3) 3 A) - 3 B) 3 C) - 27 D) not a real number 3) 4 625 A) 5 B) - 5 C) 625 D) not a real number 4) 4 ( - 3) 4 A) 3 B) - 3 C) 81 D) not a real number Simplify the radical expression. 5) 3 x 4 A) x 3 x B) x 2 3 x C) x 3 x 2 D) x 2 3 x 2 6) 3 14 · 3 4 A) 2 3 7 B) 3 56 C) 2 3 14 D) 6 56 Add or subtract terms whenever possible. 7) 2 3 40 + 3 320 A) 8 3 5 B) 2 3 360 C) 3 3 360 D) 6 3 5 8) y 3 192x - 3 24xy 3 A) 2y 3 3x B) 4y 3 3x - 192 3 3xy 3 C) (y + 1) 3 26 D) y 3 - 22xy 3 8 Understand and Use Rational Exponents MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression without using a calculator. 1) 1441/2 A) 12 B) 24 C) 6 D) 48 2) 2561/4 A) 4 B) 16 C) 64 D) 1024 3) 84/3 A) 16 B) 64 C) 32 D) 128 Page 20

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    4) 16 - 3/2 A) 1 64 B) - 1 64 C) 64 D) - 64 Simplify using properties of exponents. 5) (7x 3/4 )(10x 1/2 ) A) 70x 5/4 B) 70x 1/2 C) 70x 5/3 D) 70x 3/4 6) 50x 3/2 10x 1/3 A) 5x 7/6 B) 5x 1/3 C) 40x 1/3 D) 5x 7/2 7) (25x 4 y 6 ) 1/2 A) 5x 2 y 3 B) 625x 8 y 6 C) 5 2 x 2 y 3 D) 25x 2 y 3 Simplify by reducing the index of the radical. 8) 10 x 4 A) 5 x 2 B) x 2 C) 5 x D) x 9) 6 27x 3 A) 3x B) 3 3x C) 3 3x D) 1 9x Solve the problem. 10) The algebraic expression 0.07d 3/2 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 5 miles. Round to the nearest hundredth. A) 0.78 hours B) 0.16 hours C) 11.18 hours D) 0.21 hours 0.4 Polynomials 1 Understand the Vocabulary of Polynomials MULTIPLE 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) 4x - 1 - 8 + 7x A) No B) Yes; 7x + 4x - 1 - 8 2) 2x - 3 + 5x 2 A) Yes; 5x 2 + 2x - 3 B) No 3) 2x - 7 x A) No B) Yes; 7 x - 2 Page 21

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    4) x 2 + x 4 - x 3 + 9 A) Yes; x 4 - x 3 + x 2 + 9 B) No Find the degree of the polynomial. 5) - 6x - 8x7 - 5 A) degree 7 B) degree 8 C) degree - 6 D) degree - 8 6) - 7x + 3x 8 + 4x 7 - 16 A) degree 8 B) degree 4 C) degree 3 D) degree 7 7) - 15x4 + 2x3 + 2x - 4x5 - 3 A) degree 5 B) degree 4 C) degree - 15 D) degree 3 8) x 5 - 3x 4 y 7 + 8xy - 10x + 6 A) degree 11 B) degree 5 C) degree 18 D) degree - 3 2 Add and Subtract Polynomials MULTIPLE 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) (7x 5 + 6x 2 - 9x) + (3x 5 - 3x 2 - 9x) A) 10x 5 + 3x 2 - 18x B) - 6x 5 + 4x 2 - 3x C) 10x + 3x 5 - 18x 2 D) - 5x 8 2) (6x 4 + 9x 3 - 3x 2 - 4) + (3x 4 + 7x 3 - 9x 2 + 5) A) 9x 4 + 16x 3 - 12x 2 + 1 B) 9x 8 + 16x 6 - 12x 4 + 1 C) 13x 18 + 1 D) 3x 4 + 3x 3 + 11x 2 + 12 3) ( - 6x 5 + 18x 3 + 15) + (8x 5 + 4x 3 - 11) A) 2x 5 + 22x 3 + 4 B) 2x 5 + 10x 3 - 26 C) 2x 5 + 22x 3 - 26 D) 28x 8 4) ( - 4x 5 - 8x 4 - 2x 3 + 6) + (6x 5 + 2x 4 + 9x 3 + 5) A) 2x 5 - 6x 4 + 7x 3 + 11 B) 10x 5 + 10x 4 + 11x 3 - 1 C) 2x 5 + 10x 4 + 11x 3 - 1 D) 10x 5 + 10x 4 + 11x 3 + 11 5) (9x 5 - 16x 3 - 3) - (6x 5 - 19x 3 + 20) A) 3x 5 + 3x 3 - 23 B) 3x 5 - 10x 3 + 17 C) 3x 5 + 3x 3 + 17 D) - 17x 8 6) (4x 6 - 4x 5 + 3x 4 - 5) - (2x 6 - 2x 5 + 8x 4 - 4) A) 2x 6 - 2x 5 - 5x 4 - 1 B) 6x 6 - 6x 5 + 11x 4 - 9 C) 2x 6 - 6x 5 + 11x 4 - 9 D) 6x 6 - 6x 5 + 11x 4 - 1 7) (6x 6 + 18x 4 + 12) - (9x 6 - 4x 4 + 14) A) - 3x 6 + 22x 4 - 2 B) - 3x 6 + 27x 4 + 26 C) - 3x 6 + 22x 4 + 26 D) 17x 10 8) (4x 2 + 4x + 7) + (2x 2 + 3x + 2) - (5x + 2) A) 6x 2 + 2x + 7 B) 6x 2 + 2x + 11 C) 4x 2 + 2x + 7 D) 4x 2 + 2x + 11 Page 22

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    3 Multiply Polynomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the product. 1) (x + 2)(x 2 - 2x + 4) A) x 3 + 8 B) x 3 - 8 C) x 3 + 4x 2 + 4x + 8 D) x 3 - 4x 2 - 4x + 8 2) (x - 12)(x 2 + 2x - 7) A) x 3 - 10x 2 - 31x + 84 B) x 3 + 14x 2 + 17x - 84 C) x 3 - 10x 2 - 17x - 84 D) x 3 + 14x 2 + 31x + 84 3) (x + 6)(x 2 + 8x - 5) A) x 3 + 14x 2 + 43x - 30 B) x 4 + 6x 3 + 8x 2 + 43x - 30 C) x 3 + 14x 2 + 53x - 30 D) x 3 + 14x 2 + 53x + 30 4) (x + 4)(2x 2 + 5x + 9) A) 2x 3 + 13x 2 + 29x + 36 B) 2x 3 + 8x 2 + 20x + 36 C) 10x 3 + 25x 2 + 45x D) 40x 4 + 2x 3 + 180x 2 + 36 5) (7x - 1)(x 2 - 4x + 1) A) 7x 3 - 29x 2 + 11x - 1 B) 7x 3 - 27x 2 + 3x - 1 C) 7x 3 - 28x 2 + 7x + 1 D) 7x 3 + 29x 2 - 11x + 1 4 Use FOIL in Polynomial Multiplication MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the product. 1) (x + 9)(x - 5) A) x 2 + 4x - 45 B) x 2 - 45x + 4 C) x 2 + 3x - 45 D) x 2 + 4x + 4 2) (2x - 7)(x + 6) A) 2x 2 + 5x - 42 B) x 2 - 42x + 5 C) 2x 2 + 4x - 42 D) x 2 + 5x + 4 3) (2x - 7)(5x - 1) A) 10x2 - 37x + 7 B) 7x2 - 37x + 7 C) 10x2 - 37x - 37 D) 7x2 - 37x - 37 4) (7x 2 - 2)(9x 2 - 1) A) 63x 4 - 25x 2 + 2 B) 16x 4 - 25x 2 + 2 C) 63x 4 - 25x 2 - 25 D) 63x 2 - 25x + 2 5) (5x 3 - 2)(x 2 + 1) A) 5x 5 + 5x 3 - 2x 2 - 2 B) 5x 5 + 3x 3 - 2 C) 5x 5 + 3x 2 - 2 D) 5x 6 + 5x 3 - 2x 2 - 2 Page 23

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    Solve the problem. 6) Write a polynomial in standard form that represents the volume of the open box. x 11 - 6x 9 - 6x A) 36x 3 - 120x 2 + 99x B) 36x 3 + 120x 2 + 99x C) 36x 2 - 120x + 99 D) 6x 3 - 120x 2 + 99x 7) Write a polynomial in standard form that represents the area of the shaded region. x + 7 x + 5 x + 3 x + 2 A) 3x + 11 B) 17x + 31 C) x 2 + 14x + 11 D) - 3x - 11 5 Use Special Products in Polynomial Multiplication MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the product. 1) (x + 7)(x - 7) A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49 2) (9x + 5)(9x - 5) A) 81x2 - 25 B) x2 - 25 C) 81x2 - 90x - 25 D) 81x2 + 90x - 25 3) (3 + 11x)(3 - 11x) A) 9 - 121x 2 B) 9 - 66x - 121x 2 C) 121x 2 - 9 D) 9 + 66x - 121x 2 4) (5x 2 + 7x)(5x 2 - 7x) A) 25x 4 - 49x 2 B) 25x 4 - 70x 3 - 49x 2 C) 10x 4 - 14x 2 D) 25x 4 + 70x 3 - 49x 2 5) (1 + x 3 )(1 - x 3 ) A) 1 - x 6 B) 2 - x 6 C) 2 - x 9 D) 1 - x 9 Page 24

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    6) (12 - y 3 )(12 + y 3 ) A) 144 - y 6 B) 144 - y 9 C) 144 - y 3 D) y 6 - 144 7) (x + 3)2 A) x2 + 6x + 9 B) x2 + 9 C) 9x2 + 6x + 9 D) x + 9 8) (x - 12)2 A) x2 - 24x + 144 B) x2 + 144 C) 144x2 - 24x + 144 D) x + 144 9) (7x + 9) 2 A) 49x 2 + 126x + 81 B) 49x 2 + 81 C) 7x 2 + 126x + 81 D) 7x 2 + 81 10) (6x - 1) 2 A) 36x 2 - 12x + 1 B) 36x 2 + 1 C) 6x 2 - 12x + 1 D) 6x 2 + 1 11) (3x 2 + 4)2 A) 9x 4 + 24x 2 + 16 B) 9x 2 + 24x + 16 C) 3x 4 + 24x 2 + 16 D) 9x 4 + 16 12) (9x 2 - 2)2 A) 81x 4 - 36x 2 + 4 B) 81x 4 + 36x 2 + 4 C) 81x 4 - 36x 2 - 4 D) 81x 2 - 36x + 4 13) (5 + 3x)2 A) 25 + 30x + 9x2 B) 25 + 9x2 C) 25x 2 + 30x + 9 D) 25 + 30x + 3x2 14) (9 - 5x)2 A) 81 - 90x + 25x2 B) 81 + 25x2 C) 81x 2 - 90x + 25 D) 81 - 90x - 25x2 15) (x - 3)3 A) x3 - 9x2 + 27x - 27 B) x3 - 3x2 + 15x - 27 C) x3 - 9x2 + 15x - 27 D) x3 - 9x2 + 9x - 27 16) (3x + 5)3 A) 27x3 + 135x2 + 225x + 125 B) 27x3 + 135x2 + 135x + 125 C) 9x6 + 15x3 + 15,625 D) 9x2 + 30x + 25 17) (4x - 5)3 A) 64x3 - 240x2 + 300x - 125 B) 64x3 - 240x2 + 240x - 125 C) 64x3 + 240x2 + 300x + 125 D) 16x2 - 40x + 25 6 Perform Operations with Polynomials in Several Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Perform the indicated operations. 1) ( - 6x 2 y - xy) + (9x 2 y + 3xy) A) 3x 2 y + 2xy B) 15x 2 y + 4xy C) 3x 2 y + 4xy D) 15x 2 y + 2xy Page 25

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    2) (4x 2 y - 12xy + 10) + ( - 3x 2 y + 8xy - 5) A) x 2 y - 4xy + 5 B) - x 2 y - 20xy + 15 C) - 4x 3 y 2 + 5 D) 7x 2 y + 20xy + 15 3) (12x 4 y 2 - 7x 2 y 2 + 5xy) + (11x 4 y 2 - 8x 2 y 2 + 10xy) A) 23x 4 y 2 - 15x 2 y 2 + 15xy B) - 15x 4 y 2 + 23x 2 y 2 + 15xy C) 23x 4 y 2 + 15x 2 y 2 + 15xy D) 15x 4 y 2 - 23x 2 y 2 + 15xy 4) (x 3 + 9xy - 6y 2 ) - (8x 3 + 6xy + y 2 ) A) - 7x 3 + 3xy - 7y 2 B) 9x 3 + 3xy - 7y 2 C) - 7x 3 + 3xy - 5y 2 D) 7x 3 - 3xy - 5y 2 5) (9x 4 + 7xy - y 3 ) - (x 4 + 5xy + 7y 3 ) A) 8x 4 + 2xy - 8y 3 B) 10x 4 + 13xy + 6y 3 C) 9x 4 + 2xy - 8y 3 D) 8x 4 + 2xy - 6y 3 6) (9x 4 y 2 + 11x 3 y + 6y) - (2x 4 y 2 + 8x 3 y + 4y + 7x) A) 7x 4 y 2 + 3x 3 y + 2y - 7x B) 11x 4 y 2 + 19x 3 y + 10y + 7x C) 7x 4 y 2 - 3x 3 y + 2y - 7x D) 7x 4 y 2 + 3x 3 y + 2y + 7x Find the product. 7) (x - 11y)(x - 3y) A) x 2 - 14xy + 33y 2 B) x - 14xy + 33y C) x 2 - 14xy - 14y 2 D) x 2 - 17xy + 33y 2 8) (x + 3y)(8x - 11y) A) 8x 2 + 13xy - 33y 2 B) x 2 + 13xy - 33y 2 C) 8x 2 + 13xy + 13y 2 D) x 2 + 13xy + 13y 2 9) (6xy + 7)(7xy + 3) A) 42x 2 y 2 + 67xy + 21 B) 13x 2 y 2 + 67xy + 21 C) 42x 2 y 2 + 67xy + 67 D) 13x 2 y 2 + 67xy + 67 10) (4x + 3y)2 A) 16x2 + 24xy + 9y2 B) 16x2 + 9y2 C) 4x2 + 24xy + 9y2 D) 4x2 + 9y2 11) (3x - 11y)2 A) 9x2 - 66xy + 121y2 B) 9x2 + 121y2 C) 3x2 - 66xy + 121y2 D) 3x2 + 121y2 12) (x - y)(x 2 + xy + y 2 ) A) x 3 - y 3 B) x 3 + y 3 C) x 3 - 2x 2 y - 2xy 2 - y 3 D) x 3 + 2x 2 y + 2xy 2 - y 3 13) (x 2 y 2 + 9) 2 A) x 4 y 4 + 18x 2 y 2 + 81 B) x 2 y 2 + 18xy + 81 C) x 4 y 4 + 9x 2 y 2 + 81 D) x 4 y 4 + 81 14) (5x + 6y)(5x - 6y) A) 25x 2 - 36y 2 B) 5x 2 - 6y 2 C) 25x 2 - 60xy - 36y 2 D) 25x 2 + 60xy - 36y 2 Page 26

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    15) (3xy 2 - 13y)(3xy 2 + 13y) A) 9x 2 y 4 - 169y 2 B) 3x 2 y 4 - 13y 2 C) 9x 2 y 4 - 78xy 3 - 169y 2 D) 9x 2 y 4 + 78xy 3 - 169y 2 0.5 Factoring Polynomials 1 Factor Out the Greatest Common Factor of a Polynomial MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor out the greatest common factor. 1) 2x + 12 A) 2(x + 6) B) 2(x + 12) C) 2x(x + 6) D) 2x(6) 2) 4x 2 + 28x A) 4x(x + 7) B) x(4x + 28) C) 4(x 2 + 7x) D) 4x(x + 7x) 3) 21x 4 - 9x 3 + 12x 2 A) 3x 2 (7x 2 - 3x + 4) B) 3(7x 4 - 3x 3 + 4x 2 ) C) x 2 (21x 2 - 9x + 12) D) 3x(7x 3 - 3x 2 + 4x) 4) x(x + 13) + 5(x + 13) A) (x + 13)(x + 5) B) (x 2 + 13x) + (5x + 65) C) 5x(x + 13) D) 13x(x + 5) 5) x(5x + 4) - 2(5x + 4) A) (5x + 4)(x - 2) B) (5x + 4)(x + 2) C) (5x - 2)(x + 4) D) - 2x(5x + 4) 6) x 2 (x - 3) - (x - 3) A) (x - 3)(x 2 - 1) B) (x - 3)(x 2 + 1) C) x 2 (x - 3) D) (x 3 - 3x 2 ) - (x - 3) 2 Factor by Grouping MULTIPLE 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) x 3 - 4x 2 - 3x + 12 A) (x - 4)(x 2 - 3) B) (x - 3)(x 2 - 4) C) (x + 4)(x 2 + 3) D) (x - 4)(x - 3) 2) x 3 + 7x + 2x 2 + 14 A) (x + 2)(x 2 + 7) B) (x - 2)(x 2 + 7) C) (x + 2)(x 2 - 7) D) (x + 2)(x + 7) 3) 5x 3 - 25x 2 + 8x - 40 A) (x - 5)(5x 2 + 8) B) (x + 5)(5x 2 + 8) C) (x - 5)(5x 2 - 8) D) (x - 5)(5x + 8) 3 Factor Trinomials MULTIPLE 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 + 8x + 15 A) (x + 5)(x + 3) B) (x - 5)(x + 3) C) (x - 5)(x + 1) D) prime Page 27

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    2) x2 - 3x - 28 A) (x + 4)(x - 7) B) (x - 4)(x - 7) C) (x - 4)(x + 1) D) prime 3) x2 - 8x + 15 A) (x - 3)(x - 5) B) (x + 3)(x - 5) C) (x + 3)(x + 1) D) prime 4) x2 + 10x - 24 A) (x + 12)(x - 2) B) (x - 12)(x + 2) C) (x - 12)(x + 1) D) prime 5) x2 - x - 6 A) (x + 2)(x - 3) B) (x + 3)(x - 2) C) (x + 1)(x - 5) D) prime 6) x2 - x - 35 A) (x - 35)(x + 1) B) (x + 5)(x - 7) C) (x - 5)(x + 7) D) prime 7) 5x 2 + 18x + 16 A) (5x + 8)(x + 2) B) (5x + 2)(x + 8) C) (5x + 8)(5x + 2) D) prime 8) 7x 2 - 44x + 12 A) (7x - 2)(x - 6) B) 7(x - 2)(x - 6) C) (7x + 6)(x - 2) D) (7x - 2)(7x + 6) 9) 7x 2 + 2x - 5 A) (7x - 5)(x + 1) B) (7x + 1)(x - 5) C) (7x + 5)(x - 1) D) prime 10) 5x 2 - 3x + 2 A) (5x + 2)(x - 1) B) (5x - 1)(x + 2) C) (5x - 2)(x + 1) D) prime 11) 10x2 + 21x + 9 A) (2x + 3)(5x + 3) B) (2x - 3)(5x - 3) C) (10x + 3)(x + 3) D) prime 12) 6x2 - 17x + 12 A) (2x - 3)(3x - 4) B) (2x + 3)(3x + 4) C) (6x + 3)(x + 4) D) prime 13) 20x2 + 7x - 6 A) (4x + 3)(5x - 2) B) (4x - 3)(5x + 2) C) (20x + 3)(x - 2) D) prime 14) x2 - 2xy - 63y2 A) (x + 7y)(x - 9y) B) (x - 7y)(x - 9y) C) (x - 7y)(x + y) D) prime 15) 2x 2 + 3xy + y 2 A) (2x + y)(x + y) B) (2x - y)(x - y) C) (2x + y)(x + 2y) D) prime 16) 7x 2 - 55xy - 72y 2 A) (7x + 8y)(x - 9y) B) (7x + 9y)(x - 8y) C) y(7x + 8)(x - 9) D) prime 17) 6x2 + 13xy + 6y2 A) (3x + 2y)(2x + 3y) B) (3x - 2y)(2x - 3y) C) (6x + 2y)(x + 3y) D) prime Page 28

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    4 Factor the Difference of Squares MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the difference of two squares. 1) x 2 - 9 A) (x + 3)(x - 3) B) (x + 3) 2 C) (x - 3) 2 D) prime 2) 16x2 - 49 A) (4x + 7)(4x - 7) B) (4x - 7)2 C) (4x + 7)2 D) prime 3) 16x2 - 121y2 A) (4x + 11y)(4x - 11y) B) (4x - 11y)2 C) (4x + 11y)2 D) prime 4) x 4 - 256 A) (x 2 + 16)(x + 4)(x - 4) B) (x 2 + 16)(x 2 + 16) C) (x 2 - 16)(x 2 - 16) D) prime 5) (16x 4 - 81) A) (4x 2 + 9)(2x + 3)(2x - 3) B) (4x 2 + 9)(4x 2 - 9) C) (2x + 3) 2 (2x - 3) 2 D) (4x 2 + 9)(4x 2 + 9) 5 Factor Perfect Square Trinomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor the perfect square trinomial. 1) x2 - 10x + 25 A) (x - 5)2 B) (x + 5)2 C) (x - 5)(x + 5) D) prime 2) x2 - 20x + 400 A) (x - 20)2 B) (x + 20)2 C) (x + 20)(x - 20) D) prime 3) 36x 2 + 12x + 1 A) (6x + 1) 2 B) (6x + 1)(6x - 1) C) (x + 6) 2 D) prime 6 Factor the Sum or Difference of Two Cubes MULTIPLE 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) x 3 - 125 A) (x - 5)(x 2 + 5x + 25) B) (x + 5)(x 2 - 5x + 25) C) (x + 125)(x 2 - 1) D) prime 2) x 3 + 64 A) (x + 4)(x 2 - 4x + 16) B) (x - 4)(x 2 + 4x + 16) C) (x + 4)(x 2 + 16) D) prime Page 29

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    3) 27x 3 - 1 A) (3x - 1)(9x 2 + 3x + 1) B) (3x - 1)(9x 2 + 1) C) (3x + 1)(9x 2 - 3x + 1) D) prime 4) 8x 3 + 1 A) (2x + 1)(4x 2 - 2x + 1) B) (2x - 1)(4x 2 + 1) C) (2x - 1)(4x 2 + 2x + 1) D) prime 5) 27x 3 + 64 A) (3x + 4)(9x 2 - 12x + 16) B) (3x - 4)(9x 2 + 12x + 16) C) (3x + 4)(9x 2 + 12x + 16) D) (3x + 4)(9x 2 + 16) 6) 125x 3 - 8 A) (5x - 2)(25x 2 + 10x + 4) B) (5x + 2)(25x 2 - 10x + 4) C) (5x - 2)(25x 2 - 10x + 4) D) (5x - 2)(25x 2 + 4) 7 Use a General Strategy for Factoring Polynomials MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor completely, or state that the polynomial is prime. 1) 4x 3 - 16x A) 4x(x + 2)(x - 2) B) 4(x + 2)(x 2 - 2x) C) x(x + 2)(4x - 8) D) prime 2) 50x 2 - 32 A) 2(5x + 4)(5x - 4) B) 2(5x - 4)2 C) 2(5x + 4)2 D) prime 3) 4x 2 + 16x + 12 A) 4(x + 1)(x + 3) B) (4x + 4)(x + 3) C) (x + 1)(4x + 12) D) 4(x 2 + 4x + 3) 4) 6x 4 - 6 A) 6(x 2 + 1)(x + 1)(x - 1) B) 6(x 2 + 1)(x 2 - 1) C) 6(x + 1) 2 (x - 1) 2 D) prime 5) x 3 - 2x 2 - 25x + 50 A) (x - 2)(x + 5)(x - 5) B) (x + 2)(x + 5)(x - 5) C) (x - 2)(x - 5) 2 D) prime 6) 8x2 - 8x - 48 A) 8(x + 2)(x - 3) B) (8x + 16)(x - 3) C) prime D) 8(x - 2)(x + 3) 7) x 3 - 36x A) x(x + 6)(x - 6) B) (x 2 + 6)(x - 6) C) x(x - 6) 2 D) prime 8) 9x 3 - 9x A) 9x(x + 1)(x - 1) B) x(x + 3)(x - 3) C) 9x(x 2 + 1) D) 9x(x 2 - 1) Page 30

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