Test bank for college algebra enhanced with graphing utilities 7th edition by sullivan

Choose the one alternative that best completes the statement or answers the question.. Choose the one alternative that best completes the statement or answers the question.. Choose the o

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Ch 0 Chapter R: Review

0.1 Real Numbers

1 Work with Sets

MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question.

Use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 5, 8}, B = {2, 3, 5, 7}, and C = {1, 4, 9} to find the set.

1) B ∪ C

A) {1, 2, 3, 4, 5, 7, 9} B) { } C) {0} D) {1, 2, 3, 5, 7, 9}2) A ∪ C

A) {1, 2, 3, 4, 5, 8, 9} B) {4, 6, 7, 9} C) {1} D) {1, 2, 3, 5, 7, 9}3) A ∩ B

A) {2, 3, 5} B) {1, 2, 3, 5, 7, 8} C) {2, 3, 5, 7} D) {1, 2, 3, 5, 8}4) A ∩ C

C) {4, 6, 7, 9} D) {1, 2, 3, 5, 7, 9}

5) (A ∩ B) ∪ C

A) {1, 2, 3, 4, 5, 9} B) {1, 2, 3, 5} C) {1, 2, 3} D) {2, 3, 5}6) (B ∪ C) ∩ A

List all the elements of B that belong to the given set.

1) B = 7, 7, -14, 0, 4

5, - 5

4, 2.5Integers

A) {7, -14, 0} B) {7, 0} C) {7, -14} D) {7, 0, 7}

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2) B = 3, 5, -18, 0, 1

3, -3, 1.9Natural numbers

3) B = 11, 6, -10, 0, 0

1Real numbers

9, 0.54, 0.161616 D) 7, -8, 0, 0

9, 16, 0.54, -8 , 0.161616

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C) 8.6598.659

D) 8.6588.65911) 1.57142857

A) 1.571

1.571

B) 1.5721.571

C) 1.5711.572

D) 1.5701.572

C) 1.4441.445

D) 1.4451.445

3 Evaluate Numerical Expressions

Write the statement using symbols.

1) The sum of 9 and 3 is 12

A) 9 + 3 = 12 B) 9

3 = 3 C) 9 · 3 = 27 D) 9 - 3 = 62) The difference 70 less 14 equals 56

A) 70 - 14 = 56 B) 70

14 = 5 C) 70 + 14 = 84 D) 70 · 14 = 9803) The product of 60 and 12 equals 720

A) 60 · 12 = 720 B) 60

12 = 5 C) 60 + 12 = 72 D) 60 - 12 = 484) The quotient 18 divided by 6 is 3

A) 18

6 = 3 B) 18 · 6 = 108 C) 18 + 6 = 24 D) 18 - 6 = 12

5) The sum of four times x and 5 decreased by 7 is 8

A) 4x + 5 - 7 = 8 B) 4(x + 5) - 7 = 8 C) 7 - (4x + 5) = 8 D) 4(x + 5 - 7) = 86) Three times the difference of x and 8 is -10

A) 3(x - 8) = -10 B) 3 - x - 8 = -10 C) 3x - 8 = -10 D) 3 + x - 8 = -107) The quotient of x and the sum of 5 and x

A) x

x + 5x

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Evaluate the expression.

7

97

14) 3

5 · 1

4 + 1

8A) 9

15) 1

4 · 10 - 1

5 + 7A) 189

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21) 1

3 + 1

5 · 1

9A) 16

4 Work with Properties of Real Numbers

Use the Distributive Property to remove the parentheses.

5) (x - 11)(x - 2)

A) x2 - 13x + 22 B) x2 + 22x - 13 C) x2 - 14x + 22 D) x2 - 13x - 136) (x + 3)(x - 7)

A) x2 - 4x - 21 B) x2 - 21x - 4 C) x2 - 5x - 21 D) x2 - 4x - 47) (x + 7)(x - 7)

A) x2 - 49 B) x2 - 14 C) x2 - 14x - 49 D) x2 + 14x - 49

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0.2 Algebra Essentials

1 Graph Inequalities

On the real number line, label the points with the given coordinates.

1) -9, -7, -5, -3

-10 -10 -9 -9 -8 -8 -7 -7 -6 -6 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1

A)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

B)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1C)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

D)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

2) -4.75, -2, 0, 2.25

-5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4

A)

-5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4

B)

-5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4C)

-5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4

D)

-5 -4 -3 -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 2 3 4

B)-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

C)

-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

D)-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4

Insert <, >, or = to make the statement true.

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-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9C)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

D)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

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17) x < 4

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9A)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9B)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9C)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9D)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

18) x ≥ 4

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9A)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9B)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9C)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9D)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

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-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9C)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9D)

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

2 Find Distance on the Real Number Line

Use the given real number line to compute the distance.

1) Find d(A, B)

-5 -4 -3 -2 -1 0 1 2 3 4 5

A B

-5 -4 -3 -2 -1 0 1 2 3 4 5

A B

3 Evaluate Algebraic Expressions

Evaluate the expression using the given values.

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Use the formula C = 5

9 (F - 32) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of the Fahrenheit temperature.

13) F = 32°

Express the statement as an equation involving the indicated variables.

14) The area A of a rectangle is the product of its length l and its width w

18) The volume V of a sphere is 4

3 times times the cube of the radius r.

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19) The surface area S of a sphere is 4 times times the square of the radius r.

Solve the problem.

22) The weekly production cost C of manufacturing x calendars is given by C(x) = 20 + 6x, where the variable

C is in dollars What is the cost of producing 292 calendars?

4 Determine the Domain of a Variable

Determine which value(s), if any, must be excluded from the domain of the variable in the expression.

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7) x - 8

x - 6

5 Use the Laws of Exponents

Simplify the expression.

A) 1

6255) -5-2

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D) 1125x3

12) (x8y-1)8

A) x64

y8

B) y8x64

C) 1x64y8

C) 1x36y9

C) y2x3

D) xy2

C) 64y3343x3

D) 343y364x3

C) 49y236x2

D) 36x249y2

18) (x-6y8)-7z4

A) x42z4

y56

B) y56z4x42

C) x42y56z4

D) y56x42z4

C) 49z1464x14y4

D) 49y464x14z14

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Evaluate the expression using the given value of the variables.

6 Evaluate Square Roots

Simplify the expression.

49 D) not a real number

Find the value of the expression using the given values.

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8) yx x = -3, y = 6

A) 1

216

7 Use a Calculator to Evaluate Exponents

Use a calculator to evaluate the expression Round the answer to three decimal places.

8 Use Scientific Notation

Write the number in scientific notation.

1) 6712

A) 6.712 × 103 B) 6.712 × 104 C) 6.712 × 10-3 D) 6.712 × 1012) 237.5

A) 2.375 × 102 B) 2.375 × 10-2 C) 2.375 × 101 D) 2.375 × 10-13) 210.081

A) 2.10081 × 102 B) 2.10081 × 10-2 C) 2.10081 × 101 D) 2.10081 × 10-14) 81,000

A) 8.1 × 104 B) 8.1 × 10-4 C) 8.1 × 105 D) 8.1 × 10-55) 3,900,000

A) 3.9 × 106 B) 3.9 × 10-6 C) 3.9 × 105 D) 3.9 × 10-56) 0.000862

A) 8.62 ∘ 10-4 B) 8.62 × 104 C) 8.62 × 10-5 D) 8.62 × 10-37) 0.000093111

A) 9.3111 × 10-5 B) 9.3111 × 105 C) 9.3111 ± 10-4 D) 9.3111 × 1048) 0.0000042811

A) 4.2811 × 10-6 B) 4.2811 × 106 C) 4.2811 × 10-5 D) 4.2811 × 10-79) 0.00000016107

A) 1.6107 × 10-7 B) 1.6107 × 107 C) 1.6107 × 10-6 D) 1.6107 × 106

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10) 0.0000000487015

A) 4.87015 × 10-8 B) 4.87015 × 108 C) 4.87015 × 10-7 D) 4.87015 × 10-911) In a certain city, the subway system carried a total of 1,840,000,000 passengers

A) 1.84 × 109 B) 18.4 × 109 C) 1.84 × 108 D) 1.84 × 101012) A business projects next year's profits to be $884,000,000

A) 8.84 × 108 B) 8.84 × 107 C) 8.84 × 109 D) 8.84 × 10-913) A computer compiles a program in 0.000676 seconds

1 Use the Pythagorean Theorem and Its Converse

The lengths of the legs of a right triangle are given Find the hypotenuse.

1) a = 4, b = 3

2) a = 12, b = 16

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The lengths of the sides of a triangle are given Determine if the triangle is a right triangle If it is, identify the hypotenuse.

A) right triangle; 15 B) right triangle; 12

C) right triangle; 9 D) not a right triangle

6) 15, 36, 39

7) 21, 72, 75

8) 10, 20, 25

9) 6, 8, 12

Solve Use the fact that the radius of the Earth is 3960 miles and 1 mile = 5280 feet.

10) A guard tower at a state prison stands 103 feet tall How far can a guard see from the top of the tower?Round to the nearest tenth of a mile

11) A person who is 3 feet tall is standing on the beach and looks out onto the ocean Suddenly, a shipappears on the horizon How far is the ship from the shore? Round to the nearest tenth of a mile

2 Know Geometry Formulas

Solve the problem.

1) Find the area A of a rectangle with length 18 in and width 20 in

A) A = 360 in2 B) A = 720 in2 C) A = 38 in2 D) A = 72 in22) Find the area A of a rectangle with length 7.5 ft and width 10.4 ft

A) A = 78 ft2 B) A = 156 ft2 C) A = 17.9 ft2 D) A = 30 ft23) Find the area A of a triangle with height 3 in and base 3 in

A) A = 9

2 in2 B) A = 9

2 in C) A = 9 in2 D) A = 9 in

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4) Find the area A and circumference C of a circle of radius 7 in Express the answer in terms of

A) A = 49 in.2; C = 14 in B) A = 14 in.2; C = 14 in

C) A = 196 in.2; C = 7 in D) A = 28 in.2; C = 7 in

5) Find the area A and circumference C of a circle of diameter 11 ft Use 3.14 for Round the result to thenearest tenth

A) A = 95 ft2; C = 34.5 ft B) A = 34.5 ft2; C = 34.5 ft

C) A = 379.9 ft2; C = 17.3 ft D) A = 69.1 ft2; C = 17.3 ft

6) Find the volume V of a rectangular box with length 8 yd, width 2 yd, and height 6 yd

A) V = 96 yd3 B) V = 32 yd3 C) V = 72 yd3 D) V = 384 yd37) Find the surface area S of a rectangular box with length 3 ft, width 2 ft, and height

9) Find the volume V of a sphere of radius 2 ft Use 3.14 for If necessary, round the result to the nearesttenth

A) V = 33.5 ft3 B) V = 16.7 ft3 C) V = 18.8 ft3 D) V = 267.9 ft310) Find the volume V of a right circular cylinder with radius 7 ft and height 16 ft Express the answer in terms

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13) Find the area of the shaded region Express the answer in terms of

11

A) 2 - 4 square units B) 1 - 4 square units

C) 4 square units D) 2 - 2 square units

16) A bicycle wheel makes 4 revolutions Determine how far the bicycle travels in inches if the diameter of thewheel is 13 in Use ≈ 3.14 Round to the nearest tenth

17) A rectangular patio has dimensions 10 feet by 15 feet The patio is surrounded by a border with a uniformwidth of 2 feet Find the area of the border

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18) A circular swimming pool, 20 feet in diameter, is enclosed by a circular deck that is 4 feet wide What is thearea of the deck? Use = 3.1416.

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3 Understand Congruent Triangles and Similar Triangles

The triangles are similar Find the missing length x and the missing angles A, B, C.

139°

A) x = 15; A = 27; B = 14; C = 139 B) x = 30; A = 14; B = 27; C = 139

C) x = 15; A = 139; B = 14; C = 27 D) x = 30; A = 27; B = 14; C = 139

Solve If necessary, round to the nearest tenth.

3) A flagpole casts a shadow of 33 feet Nearby, a 5-foot tree casts a shadow of 2 feet What is the height ofthe flagpole?

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6) If a tree 32.5 feet tall casts a shadow that is 13 feet long, find the height of a tree casting a shadow that is 25feet long.

0.4 Polynomials

1 Recognize Monomials

Tell whether the expression is a monomial If it is, name the variable(s) and coefficient, and give the degree of the monomial.

1) -18x

A) Monomial; variable x; coefficient -18; degree 1

B) Monomial, variable x; coefficient 1; degree -18

C) Monomial,; variable x; coefficient -18; degree 0

A) Monomial; variable x; coefficient -11; degree -3

B) Monomial; variable x; coefficient 3; degree -11

C) Monomial; variable x; coefficient -11; degree 3

D) Not a monomial

5) -3xy7

A) Monomial; variables x, y; coefficient -3; degree 8

B) Monomial; variables x, y; coefficient -3; degree 7

C) Monomial; variables x, y; coefficient -3; degree 1

D) Not a monomial

6) 7x2y6

A) Monomial; variables x, y; coefficient 7; degree 8

B) Monomial; variables x, y; coefficient 7; degree 2

C) Monomial; variables x, y; coefficient 7; degree 6

D) Not a monomial

7) 20x

y

A) Monomial; variables x, y; coefficient 20; degree 1

B) Monomial; variables x, y; coefficient 20; degree -2

C) Monomial; variables x, y; coefficient 20; degree 2

D) Not a monomial

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8) - -3x7

y3

A) Monomial; variables x, y; coefficient -3; degree 7

B) Monomial; variables x, y; coefficient -3; degree 3

C) Monomial; variables x, y; coefficient -3; degree 4

Tell whether the expression is a polynomial If it is, give its degree.

1) 7x5 - 2

A) Polynomial; degree 5 B) Polynomial; degree 2

C) Polynomial; degree 7 D) Not a polynomial

2) 1 - 5x

C) Polynomial; degree -5 D) Not a polynomial

3) 18

A) Polynomial, degree 0 B) Polynomial, degree 1

C) Polynomial, degree 18 D) Not a polynomial

4) 7

A) polynomial, degree 0 B) polynomial, degree 1

C) polynomial, degree 7 D) not a polynomial

5) 7x5 - 2

xA) Polynomial; degree 5 B) Polynomial; degree -1

6) 14

x + 1

A) Polynomial, degree 0 B) Polynomial, degree -1

C) Polynomial, degree 14 D) Not a Polynomial

7) -6y8 - 3

A) Polynomial; degree 8 B) Polynomial; degree -6

8) 8z3 + z

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9) -6x6 - 18x4

-3x2

3 Add and Subtract Polynomials

Add or subtract as indicated Express the answer as a single polynomial in standard form.

1) (8x2 + 3x - 13) + (6x + 13)

A) 8x2 + 9x B) 8x2 + 9x - 26 C) 8x2 + 3x + 26 D) 17x3

2) (8x2 - 6x - 5) + (8x2 + 8x - 3)

A) 16x2 + 2x - 8 B) 3x2 + 16x - 9 C) 16x2 - 2x - 8 D) 16x2 + 2x + 83) (8x2 + 14x - 6) - (3x2 + 9x - 18)

A) 5x2 + 5x + 12 B) 5x2 + 17x - 24 C) 5x2 + 5x - 24 D) 5x2 + 5x - 124) (7x4 - 8x3) + (2x4 - 5x3)

A) -46x3 + 4x2 - 10x - 14 B) -46x3 + 4x2 + 10x - 14

C) -46x3 + x2 - 10x - 14 D) -46x3 + 4x2 - 10x + 14

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13) (x2 + 1) - (9x2 + 5) + (x2 + x - 2)

A) -7x2 + x - 6 B) -9x2 + x - 6 C) -8x2 + x - 6 D) -7x2 + 6x - 114) -9(1 - y3) - 3(1 + y + y2 + y3)

A) 6y3 - 3y2 - 3y - 12 B) 6y3 + 3y2 - 3y + 12

C) 6y3 - 3 - ay2 - 3y - 12 D) -6y3 - 3y2 - 3y - 12

4 Multiply Polynomials

Perform the indicated operations Express the answer as a single polynomial in standard form.

1) 10x(-2x + 6)

A) -20x2 + 60x B) 40x2 C) -20x2 + 6x D) -2x2 + 60x2) -6x4(12x + 9)

A) 20y3 + 2y2 - 92y - 77 B) 20y3 - 20y2 - 70y + 11

C) 42y2 - 42y - 147 D) 20y3 + 42y2 + 92y + 77

Multiply the polynomials using the FOIL method Express the answer as a single polynomial in standard form.

7) (x + 9)(x + 3)

A) x2 + 12x + 27 B) x2 + 27x + 12 C) x2 + 11x + 27 D) x2 + 12x + 128) (-2x - 11)(x + 3)

A) -2x2 - 17x - 33 B) -2x2 - 33x - 17 C) -2x2 - 17x - 17 D) -2x2 - 19x - 339) (3x + 5)(5x + 9)

A) 15x2 + 52x + 45 B) 8x2 + 52x + 45 C) 15x2 + 52x + 52 D) 8x2 + 52x + 5210) (x - 3y)(x + 11y)

A) x2 + 8xy - 33y2 B) x + 8xy - 33y C) x2 + 8xy + 8y2 D) x2 + 5xy - 33y2

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11) (x - 9y)(3x - 12y)

A) 3x2 - 39xy + 108y2 B) x2 - 39xy + 108y2

C) 3x2 - 39xy - 39y2 D) x2 - 39xy - 39y2

12) (3x + 6y)(-5x - 12y)

A) -15x2 - 66xy - 72y2 B) -15x2 - 30xy - 72y2

C) -15x2 - 36xy - 72y2 D) -15x2 - 66xy - 66y2

5 Know Formulas for Special Products

Multiply the polynomials Express the answer as a single polynomial in standard form.

1) (x + 10)(x - 10)

A) x2 - 100 B) x2 - 20 C) x2 - 20x - 100 D) x2 + 20x - 1002) (10x + 13)(10x - 13)

A) 36x2 - 60xy + 25y2 B) 36x2 + 25y2

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6 Divide Polynomials Using Long Division

Find the quotient and the remainder.

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7 Work with Polynomials in Two Variables

Multiply the polynomials using the FOIL method Express the answer as a single polynomial in standard form.

1) (x - 2y)(x + 9y)

A) x2 + 7xy - 18y2 B) x + 7xy - 18y C) x2 + 7xy + 7y2 D) x2 + 4xy - 18y22) (-3x + 7y)(-3x - 4y)

A) 9x2 - 9xy - 28y2 B) 9x2 - 21xy - 28y2 C) 9x2 + 12xy - 28y2 D) 9x2 - 9xy - 9y2

Multiply the polynomials using the special product formulas Express the answer as a single polynomial in standard form.

3) (x + 3y)(x - 3y)

A) x2 - 9y2 B) x2 - 6y2 C) x2 - 6xy - 9y2 D) x2 + 6xy - 9y24) (6x + y)(6x - y)

A) 36x2 - y2 B) 12x2 - y2 C) 36x2 - 12xy - y2 D) 36x2 + 12xy - y25) (5x + 9y)(5x - 9y)

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6) (x - y)2

A) x2 - 2xy + y2 B) x2 - xy + y2 C) x2 - y2 D) x2 - 2x2y2 + y27) (x - 3y)2

A) x2 - 6xy + 9y2 B) x2 - 3xy + 9y2 C) x2 - y2 D) x2 + 6xy + 9y28) (4x - y)2

A) 16x2 - 8xy + y2 B) 16x2 - 4xy + y2 C) 16x2 + y2 D) 16x2 - 8xy - 2y29) (2x + 7y)2

A) 4x2 + 28xy + 49y2 B) 4x2 + 49y2 C) 2x2 + 28xy + 49y2 D) 2x2 + 49y210) (10x - 11y)2

A) 100x2 - 220xy + 121y2 B) 100x2 + 121y2

C) 10x2 - 220xy + 121y2 D) 10x2 + 121y2

0.5 Factoring Polynomials

1 Factor the Difference of Two Squares and the Sum and Difference of Two Cubes

Factor the polynomial by removing the common monomial factor.

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9) 64y3 - 1

A) (4y - 1)(16y2 + 4y + 1) B) (4y - 1)(16y2 + 1)

C) (64y - 1)(y2 + 4y + 1) D) (4y + 1)(16y2 - 4y + 1)

A) (x2 + 11)(x2 - 11) B) (x2 + 11)2 C) (x2 - 11)2 D) prime17) x4 - 16

A) (x2 + 4)(x + 2)(x - 2) B) (x2 + 4)2

18) (x + 6)2 - 49

A) (x + 13)(x - 1) B) (x + 55)(x - 43) C) (x + 1)(x - 13) D) x2 + 12x - 1319) (x - 2)2 - 64

A) (x + 6)(x - 10) B) (x + 62)(x - 66) C) (x - 6)(x + 10) D) (x - 10)220) x9 + 1

A) (x + 1)(x2 - x + 1)(x6 - x3 + 1) B) (x3 + 1)(x6 - x3 + 1)

C) (x - 1)(x2 + x + 1)(x6 + x3 + 1) D) (x - 1)(x + 1)(x6 - x3 + 1)

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2 Factor Perfect Squares

Factor the perfect square.

1) x2 + 30x + 225

A) (x + 15)2 B) (x - 15)2 C) (x + 15)(x - 15) D) x2 + 30x + 2252) x2 + 8x + 16

A) (x + 4)2 B) (x + 4)(x - 4) C) (x - 4)2 D) (x + 8)(x - 8)3) 16x2 - 72x + 81

A) (4x - 9)2 B) (4x + 9)2 C) (4x + 9)(4x - 9) D) (4x - 10)24) 4x2 + 20x + 25

A) (2x + 5)2 B) (2x - 5)2 C) (2x + 5)(2x - 5) D) (2x - 6)25) x4 + 4x2 + 4

3 Factor a Second-Degree Polynomial: x^2 + Bx + C

Factor the polynomial.

1) x2 - x - 30

A) (x + 5)(x - 6) B) (x + 6)(x - 5) C) (x + 1)(x - 30) D) prime

2) x2 - 12x + 27

A) (x - 3)(x - 9) B) (x + 3)(x - 9) C) (x + 3)(x + 1) D) prime

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Factor the polynomial by grouping.

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7) 2y3 + 6y2 - 4y2 - 12y

A) 2y(y + 3)(y - 2) B) (y + 3)(y - 2) C) (y + 3)(2y2 - 4y) D) 2y(y - 3)(y + 2)8) 15x6 - 12x3 + 20x3 - 16

A) (3x3 + 4)(5x3 - 4) B) (3x3 - 4)(5x3 + 4) C) (3x6 + 4)(5x - 4) D) (15x3 - 4)(x3 + 4)9) 15x2 - 6xy + 10xy - 4y2

A) (3x + 2y)(5x - 2y) B) (3x + 2)(5x - 2) C) (3x - 2y)(5x - 2y) D) (15x + 2y)(x - 2y)10) 15x3 - 10x2y - 9xy2 + 6y3

A) (5x2 - 3y2)(3x - 2y) B) (5x2 - 3y)(3x - 2y)

C) (5x2 + 3y2)(3x + 2y) D) (15x2 - 3y2)(x - 2y)

An expression that occurs in calculus is given Factor completely.

5 Factor a Second-Degree Polynomial: Ax^2 + Bx + C, A ≠ 1

Factor the polynomial.

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Factor completely If the polynomial cannot be factored, say it is prime.

A) (3x2 + 4)(5x2 + 2) B) (5x2 - 2)(3x2 - 4) C) (3x2 + 1)(5x2 + 8) D) (15x2 + 4)(x2 + 2)16) 9x4 - 6x2 - 8

A) (3x2 - 4)(3x2 + 2) B) (3x - 2)(3x + 4) C) (3x2 + 1)(3x2 - 8) D) (9x2 - 4)(x2 + 2)17) 6x6 + 5x3 - 6

A) (2x3 + 3)(3x3 - 2) B) (3x3 + 2)(2x3 - 3) C) 6(x3 - 2)(x3 + 3) D) (2x3 + 1)(3x3 - 6)18) 7y6 - 44y3 + 45

A) (7y3 - 9)(y3 - 5) B) y2(7y2 - 9)(y2 - 5)

C) y4(7y - 9)(y - 5) D) (7y3 - 5y2 + y - 9)(y3 - 9y2 + y - 5)

6 Complete the Square

What number should be added to complete the square of the expression?

1) x2 + 14x

2) x2 - 6x

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