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College Algebra | 7th Edition | ISBN: 9781439048610 | Authors: Richard N. Aufmann, Vernon C. Barker, Richard D. Nation
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Author: Richard N. Aufmann, Vernon C. Barker, Richard D. Nation
Publisher: Cengage Learning
ISBN: 9781439048610
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Chapter Problems

Chapter: Problem: 3.4.1

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = x4 + x3 - 2x2 + 4x - 24

Chapter: Problem: 3.1.1

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 5x3 + 6x2 - 17x + 20, x + 3

Chapter: Problem: 3.5.1

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 1 x

Chapter: Problem: 3.2.1

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = 3x4 - 2x 2 - 7x + 1

Chapter: Problem: 1

College Algebra 7
In Exercises 1 and 2, use synthetic division to divide the first polynomial by the second. 4x3 - 11x2 + 5x - 2, x - 3

Chapter: Problem: 3.3.1

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (x - 3)2 (x + 5)

Chapter: Problem: 3.4.2

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = x3 - 3x2 + 7x - 5

Chapter: Problem: 3.1.2

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 6x3 + 15x2 - 8x + 2, x + 4

Chapter: Problem: 3.5.2

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 2 x - 3

Chapter: Problem: 3.2.2

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = -2x 3 - 6x 2 + 5x - 1

Chapter: Problem: 2

College Algebra 7
In Exercises 1 and 2, use synthetic division to divide the first polynomial by the second. x4 + 9x3 + 6x2 - 65x - 63, x + 7

Chapter: Problem: 3.3.2

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (x + 4)3 (x - 1)2

Chapter: Problem: 3.4.3

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x4 - x3 - 4x2 + 10x - 4

Chapter: Problem: 3.1.3

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. x4 - 5x2 + 3x - 1, x - 2

Chapter: Problem: 3.5.3

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = x2 - 3 x2 + 1

Chapter: Problem: 3.2.3

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = 5x5 - 4x 3 - 17x 2

Chapter: Problem: 3

College Algebra 7
In Exercises 3 to 6, use the Remainder Theorem to find P(c). P(x) = x3 + 2x2 - 5x + 1, c = 4

Chapter: Problem: 3.3.3

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = x2 (3x + 5)2

Chapter: Problem: 3.4.4

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = x3 - 13x2 + 65x - 125

Chapter: Problem: 3.1.4

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. x4 - 5x3 + x - 4, x - 1

Chapter: Problem: 3.5.4

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = x3 + 4 x2 - 25

Chapter: Problem: 3.2.4

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = -6x4 - 3x 3 + 5x 2 - 2x + 5

Chapter: Problem: 4

College Algebra 7
In Exercises 3 to 6, use the Remainder Theorem to find P(c). P(x) = -4x3 - 10x + 8, c = -1

Chapter: Problem: 3.3.4

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = x3 (2x + 1)(3x - 12)2

Chapter: Problem: 3.4.5

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = x5 - 9x4 + 34x3 - 58x2 + 45x - 13

Chapter: Problem: 3.1.5

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. x2 + x3 - 2x - 5, x - 3

Chapter: Problem: 3.5.5

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 2x - 1 2x2 - 15x + 18

Chapter: Problem: 3.2.5

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = 2 - 3x - 4x 2

Chapter: Problem: 5

College Algebra 7
In Exercises 3 to 6, use the Remainder Theorem to find P(c). P(x) = 6x4 - 12x2 + 8x + 1, c = -2

Chapter: Problem: 3.3.5

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (x2 - 4)(x + 3)2

Chapter: Problem: 3.4.6

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = x4 - 4x3 + 53x2 - 196x + 196

Chapter: Problem: 3.1.6

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 4x + 3x2 + x3 - 5, x - 2

Chapter: Problem: 3.5.6

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 3x - 2 4x2 - 27x + 18

Chapter: Problem: 3.2.6

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = -16 + x4

Chapter: Problem: 6

College Algebra 7
In Exercises 3 to 6, use the Remainder Theorem to find P(c). P(x) = 5x5 - 8x4 + 2x3 - 6x2 - 9, c = 3

Chapter: Problem: 3.3.6

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (x + 4)3 (x2 - 9)2

Chapter: Problem: 3.4.7

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x4 - x3 - 15x2 + 23x + 15

Chapter: Problem: 3.1.7

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 2x4 + 5x3 - 6x2 + 4x + 3, 2x2 - x + 1

Chapter: Problem: 3.5.7

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 2x2 x3 - 4x2 - 12x

Chapter: Problem: 3.2.7

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = 1 2 (x3 + 5x2 - 2)

Chapter: Problem: 7

College Algebra 7
In Exercises 7 to 10, use synthetic division to show that c is a zero of the given polynomial function. P(x) = x3 + 2x2 - 26x + 33, c = 3

Chapter: Problem: 3.3.7

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (3x - 5)2 (2x - 7)

Chapter: Problem: 3.4.8

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 3x4 - 17x3 - 39x2 + 337x + 116

Chapter: Problem: 3.1.8

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 3x3 + x2 - 5x + 2, x2 - 2x + 2

Chapter: Problem: 3.5.8

College Algebra 7
In Exercises 1 to 8, determine the domain of the rational function. F(x) = 3x2 x2 - 5

Chapter: Problem: 3.2.8

College Algebra 7
In Exercises 1 to 8, examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function. P(x) = - 1 4 (x4 + 3x 2 - 2x + 6)

Chapter: Problem: 8

College Algebra 7
In Exercises 7 to 10, use synthetic division to show that c is a zero of the given polynomial function. P(x) = 2x4 + 8x3 - 8x2 - 31x + 4, c = -4

Chapter: Problem: 3.3.8

College Algebra 7
In Exercises 1 to 8, find the zeros of the polynomial function and state the multiplicity of each zero. P(x) = (5x - 2)(x + 3)4

Chapter: Problem: 3.4.9

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x4 - 14x3 + 33x2 - 46x + 40

Chapter: Problem: 3.1.9

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. 2x5 - x3 + 5x2 - 9x + 6, 2x2 + 2x - 3

Chapter: Problem: 3.5.9

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = 2x - 1 x2 + 3x

Chapter: Problem: 3.2.9

College Algebra 7
The following graph is the graph of a third-degree (cubic) polynomial function. What does the far-left and far-right behavior of the graph say about the leading coefficient a? 5 5 7.5 P(x) = ax3 + bx2 + cx + d

Chapter: Problem: 9

College Algebra 7
In Exercises 7 to 10, use synthetic division to show that c is a zero of the given polynomial function. P(x) = x5 - x4 - 2x2 + x + 1, c = 1

Chapter: Problem: 3.3.9

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = x3 + 3x2 - 6x - 8

Chapter: Problem: 3.4.10

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 3x4 - 10x3 + 15x2 + 20x - 8

Chapter: Problem: 3.1.10

College Algebra 7
In Exercises 1 to 10, use long division to divide the first + 4, x - 2 polynomial by the second. x5 + 3x4 - 2x3 - 7x2 - x + 4, x2 + 1

Chapter: Problem: 3.5.10

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = 3x2 + 5 x2 - 4

Chapter: Problem: 3.2.10

College Algebra 7
The following graph is the graph of a fourth-degree (quartic) polynomial function. What does the far-left and far-right behavior of the graph say about the leading coefficient a? = ax4 + bx3 + cx2 + dx + e 5 5 5

Chapter: Problem: 10

College Algebra 7
In Exercises 7 to 10, use synthetic division to show that c is a zero of the given polynomial function. P(x) = 2x3 + 3x2 - 8x + 3, c = 1 2

Chapter: Problem: 3.3.10

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = x3 - 19x - 30

Chapter: Problem: 3.4.11

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x3 - 9x2 + 18x - 20

Chapter: Problem: 3.1.11

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 4x3 - 5x2 + 6x - 7, x - 2

Chapter: Problem: 3.5.11

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = x2 + 11 6x2 - 5x - 4

Chapter: Problem: 3.2.11

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 11

College Algebra 7
In Exercises 11 and 12, use the Factor Theorem to determine whether the given binomial is a factor of P. P(x) = x3 - 11x2 + 39x - 45, (x - 5)

Chapter: Problem: 3.3.11

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = 2x3 + x2 - 25x + 12

Chapter: Problem: 3.4.12

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 3x4 - 19x3 + 59x2 - 79x + 36

Chapter: Problem: 3.1.12

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 5x3 + 6x2 - 8x + 1, x - 5

Chapter: Problem: 3.5.12

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = 3x - 5 x3 - 8

Chapter: Problem: 3.2.12

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 12

College Algebra 7
In Exercises 11 and 12, use the Factor Theorem to determine whether the given binomial is a factor of P. P(x) = 2x4 - 11x3 + 11x2 - 33x + 15, (x + 2)

Chapter: Problem: 3.3.12

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = 3x3 + 11x2 - 6x - 8

Chapter: Problem: 3.4.13

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x4 - x3 - 2x2 + 13x - 6

Chapter: Problem: 3.1.13

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 4x3 - 2x + 3, x + 1

Chapter: Problem: 3.5.13

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = 5x2 - 3 4x3 - 25x2 + 6x

Chapter: Problem: 3.2.13

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 13

College Algebra 7
In Exercises 13 and 14, determine the far-left and the far-right behavior of the graph of the function. P(x) = -2x3 - 5x2 + 6x - 3

Chapter: Problem: 3.3.13

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = 6x4 + 23x3 + 19x2 - 8x - 4

Chapter: Problem: 3.4.14

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 4x4 - 4x3 + 13x2 - 12x + 3

Chapter: Problem: 3.1.14

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 6x3 - 4x2 + 17, x + 3

Chapter: Problem: 3.5.14

College Algebra 7
In Exercises 9 to 14, find all vertical asymptotes of each rational function. F(x) = 5x x4 - 81

Chapter: Problem: 3.2.14

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 14

College Algebra 7
In Exercises 13 and 14, determine the far-left and the far-right behavior of the graph of the function. P(x) = -x4 + 3x3 - 2x2 + x - 5

Chapter: Problem: 3.3.14

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = 2x3 + 9x2 - 2x - 9

Chapter: Problem: 3.4.15

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 3x5 + 2x4 + 10x3 + 6x2 - 25x - 20

Chapter: Problem: 3.1.15

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. x5 - 10x3 + 5x - 1, x - 4

Chapter: Problem: 3.5.15

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = 4x2 + 1 x2 + x + 1

Chapter: Problem: 3.2.15

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 15

College Algebra 7
In Exercises 15 and 16, use the maximum and minimum features of a graphing utility to estimate, to the nearest thousandth, the x and y coordinates of the points where P has a relative maximum or a relative minimum. P(x) = 2x3 - x2 - 3x + 1

Chapter: Problem: 3.3.15

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = 4x4 - 12x3 - 3x2 + 12x - 7

Chapter: Problem: 3.4.16

College Algebra 7
In Exercises 1 to 16, find all the zeros of the polynomial function and write the polynomial as a product of its leading coefficient and its linear factors. (Hint: First determine the rational zeros.) P(x) = 2x6 - 11x5 + 5x4 + 60x3 - 62x2 - 64x + 40

Chapter: Problem: 3.1.16

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 6x4 - 2x3 - 3x2 - x, x - 5

Chapter: Problem: 3.5.16

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = 3x3 - 27x2 + 5x - 11 x5 - 2x3 + 7

Chapter: Problem: 3.2.16

College Algebra 7
In Exercises 11 to 16, use a graphing utility to graph each polynomial. Use the maximum and minimum features of the graphing utility to estimate, to the nearest tenth, the coordinates of the points where P(x) has a relative maximum or a relative minimum. For each point, indicate whether the y value i

Chapter: Problem: 16

College Algebra 7
In Exercises 15 and 16, use the maximum and minimum features of a graphing utility to estimate, to the nearest thousandth, the x and y coordinates of the points where P has a relative maximum or a relative minimum. P(x) = x4 - 2x2 + x + 1

Chapter: Problem: 3.3.16

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = x5 - x4 - 7x3 + 7x2 - 12x - 12

Chapter: Problem: 3.4.17

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = 2x3 - 5x2 + 6x - 2; 1 + i

Chapter: Problem: 3.1.17

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. x5 - 1, x - 1

Chapter: Problem: 3.5.17

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = 15,000x3 + 500x - 2000 700 + 500x3

Chapter: Problem: 3.2.17

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = x3 - 2x2 - 15x (3)

Chapter: Problem: 17

College Algebra 7
In Exercises 17 and 18, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 3x a = 2, b = 3 3 - 7x2 - 3x + 7

Chapter: Problem: 3.3.17

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = x5 - 32

Chapter: Problem: 3.4.18

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = 3x3 - 29x2 + 92x + 34; 5 + 3i

Chapter: Problem: 3.1.18

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. x4 + 1, x + 1

Chapter: Problem: 3.5.18

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = 6000a1 - 25 (x + 5)2 b

Chapter: Problem: 3.2.18

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = x3 - 6x2 + 8x (3)

Chapter: Problem: 18

College Algebra 7
In Exercises 17 and 18, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 3x a = -2, b = -1 4 - 5x3 - 6x2 - 10x - 24

Chapter: Problem: 3.3.18

College Algebra 7
In Exercises 9 to 18, use the Rational Zero Theorem to list possible rational zeros for each polynomial function. P(x) = x4 - 1

Chapter: Problem: 3.4.19

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x3 + 3x2 + x + 3; -i

Chapter: Problem: 3.1.19

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 8x3 - 4x2 + 6x - 3, x - 1 2

Chapter: Problem: 3.5.19

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = 4x2 - 11x + 6 4 - x + 1 3 x2

Chapter: Problem: 3.2.19

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = x4 - 13x2 + 36 (4)

Chapter: Problem: 19

College Algebra 7
In Exercises 19 and 20, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of (x c) Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (x + 3)(x - 5)2

Chapter: Problem: 3.3.19

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = x3 + 3x2 - 6x - 6

Chapter: Problem: 3.4.20

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x4 - 6x3 + 71x2 - 146x + 530; 2 + 7i

Chapter: Problem: 3.1.20

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 12x3 + 5x2 + 5x + 6, x + 3 4

Chapter: Problem: 3.5.20

College Algebra 7
In Exercises 15 to 20, find the horizontal asymptote of each rational function. F(x) = (2x - 3)(3x + 4) (1 - 2x)(3 - 5x)

Chapter: Problem: 3.2.20

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = 4x4 - 37x2 + 9 (4)

Chapter: Problem: 20

College Algebra 7
In Exercises 19 and 20, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of (x c) Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (x - 4)4 (x + 1)

Chapter: Problem: 3.3.20

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = x3 - 19x - 28

Chapter: Problem: 3.4.21

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x4 - 4x3 + 14x2 - 4x + 13; 2 - 3i

Chapter: Problem: 3.1.21

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. x8 + x6 + x4 + x2 + 4, x - 2

Chapter: Problem: 3.5.21

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1 x + 4

Chapter: Problem: 3.2.21

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = x5 - 5x3 + 4x (5)

Chapter: Problem: 21

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = x3 - x

Chapter: Problem: 3.3.21

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = 2x3 + x2 - 25x + 10

Chapter: Problem: 3.4.22

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x5 - 6x4 + 22x3 - 64x2 + 117x - 90; 3i

Chapter: Problem: 3.1.22

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. -x7 - x5 - x3 - x - 5, x + 1

Chapter: Problem: 3.5.22

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1 x - 2

Chapter: Problem: 3.2.22

College Algebra 7
In Exercises 17 to 22, find the real zeros of each polynomial function by factoring. The number in parentheses to the right of each polynomial indicates the number of real zeros of the given polynomial function. P(x) = x5 - 25x3 + 144x (5)

Chapter: Problem: 22

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = -x3 - x2 + 8x + 12

Chapter: Problem: 3.3.22

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = 3x3 + 11x2 - 6x - 9

Chapter: Problem: 3.4.23

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x4 - 4x3 + 19x2 - 30x + 50; 1 + 3i

Chapter: Problem: 3.1.23

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. x6 + x - 10, x + 3

Chapter: Problem: 3.5.23

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = -4 x - 3

Chapter: Problem: 3.2.23

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 2x3 + 3x2 - 23x - 42; a = 3, b = 4

Chapter: Problem: 23

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = x4 - 6

Chapter: Problem: 3.3.23

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = 6x4 + 23x3 + 19x2 - 8x - 4

Chapter: Problem: 3.4.24

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x5 - x4 - 4x3 - 4x2 - 5x - 3; i

Chapter: Problem: 3.1.24

College Algebra 7
In Exercises 11 to 24, use synthetic division to divide the first polynomial by the second. 2x5 - 3x4 - 5x2 - 10, x - 4

Chapter: Problem: 3.5.24

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = -3 x + 2

Chapter: Problem: 3.2.24

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 4x3 - x2 - 6x + 1; a = 0, b = 1

Chapter: Problem: 24

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = x5 - x

Chapter: Problem: 3.3.24

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = -2x3 - 9x2 + 2x + 9

Chapter: Problem: 3.4.25

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x5 - 3x4 + 7x3 - 13x2 + 12x - 4; -2i

Chapter: Problem: 3.1.25

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = 3x3 + x2 + x - 5, c = 2

Chapter: Problem: 3.5.25

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 4 x

Chapter: Problem: 3.2.25

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 3x3 + 7x2 + 3x + 7; a = -3, b = -2

Chapter: Problem: 25

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = x4 - 10x2 + 9

Chapter: Problem: 3.3.25

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = -4x4 + 12x3 + 3x2 - 12x + 7

Chapter: Problem: 3.3.26

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = x5 - x4 - 7x3 + 7x2 - 12x - 12

Chapter: Problem: 3.4.26

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x4 - 8x3 + 18x2 - 8x + 17; i

Chapter: Problem: 3.1.26

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = 2x3 - x2 + 3x - 1, c = 3

Chapter: Problem: 3.5.26

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = -4 x

Chapter: Problem: 3.2.26

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 2x3 - 21x2 - 2x + 25; a = 1, b = 2

Chapter: Problem: 26

College Algebra 7
In Exercises 21 to 26, graph the polynomial function. P(x) = x5 - 5x3

Chapter: Problem: 3.3.27

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = x5 - 32

Chapter: Problem: 3.4.27

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = x4 - 17x3 + 112x2 - 333x + 377; 5 + 2i

Chapter: Problem: 3.1.27

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = 4x4 - 6x2 + 5, c = -2

Chapter: Problem: 3.5.27

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x x + 4

Chapter: Problem: 3.2.27

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 4x4 + 7x3 - 11x2 + 7x - 15; a = 1, b = 1 1 2

Chapter: Problem: 27

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = x3 - 7x - 6

Chapter: Problem: 3.3.28

College Algebra 7
In Exercises 19 to 28, find the smallest positive integer and the largest negative integer that, by the Upper- and Lower-Bound Theorem, are upper and lower bounds for the real zeros of each polynomial function. P(x) = x4 - 1

Chapter: Problem: 3.4.28

College Algebra 7
In Exercises 17 to 28, use the given zero to find the remaining zeros of each polynomial function. P(x) = 2x5 - 8x4 + 61x3 - 99x2 + 12x + 182; 1 - 5i

Chapter: Problem: 3.1.28

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = 6x3 - x2 + 4x, c = -3

Chapter: Problem: 3.5.28

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x x - 2

Chapter: Problem: 3.2.28

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = 5x3 - 16x2 - 20x + 64; a = 3, b = 3 1 2

Chapter: Problem: 28

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = 2x3 + 3x2 - 29x - 30

Chapter: Problem: 3.3.29

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x3 + 3x2 - 6x - 8

Chapter: Problem: 3.4.29

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. 2x3 - x2 + x - 6 = 0

Chapter: Problem: 3.1.29

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = -2x3 - 2x2 - x - 20, c = 10

Chapter: Problem: 3.5.29

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x + 4 2 - x

Chapter: Problem: 3.2.29

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = x4 - x2 - x - 4; a = 1.7, b = 1.8

Chapter: Problem: 29

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = 15x3 - 91x2 + 4x + 12

Chapter: Problem: 3.3.30

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x3 - 19x - 30

Chapter: Problem: 3.4.30

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. 4x3 + 3x2 + 16x + 12 = 0

Chapter: Problem: 3.1.30

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = -x3 + 3x2 + 5x + 30, c = 8

Chapter: Problem: 3.5.30

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x + 3 1 - x

Chapter: Problem: 3.2.30

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = x3 - x - 8; a = 2.1, b = 2.2

Chapter: Problem: 30

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = x4 - 12x3 + 52x2 - 96x + 64

Chapter: Problem: 3.3.31

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 2x3 + x2 - 25x + 12

Chapter: Problem: 3.4.31

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. 24x3 - 62x2 - 7x + 30 = 0

Chapter: Problem: 3.1.31

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = -x4 + 1, c = 3

Chapter: Problem: 3.5.31

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1 x2 - 9

Chapter: Problem: 3.2.31

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = -x4 + x3 + 5x - 1; a = 0.1, b = 0.2

Chapter: Problem: 31

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = x3 + x2 - x - 1

Chapter: Problem: 3.3.32

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 3x3 + 11x2 - 6x - 8

Chapter: Problem: 3.4.32

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. 12x3 - 52x2 + 27x + 28 = 0

Chapter: Problem: 3.1.32

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = x5 - 1, c = 1

Chapter: Problem: 3.5.32

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = -2 x2 - 4

Chapter: Problem: 3.2.32

College Algebra 7
In Exercises 23 to 32, use the Intermediate Value Theorem to verify that P has a zero between a and b. P(x) = -x3 - 2x2 + x - 3; a = -2.8, b = -2.7

Chapter: Problem: 32

College Algebra 7
In Exercises 27 to 32, use the Rational Zero Theorem to list all possible rational zeros for each polynomial function. P(x) = 6x5 + 3x - 2

Chapter: Problem: 3.3.33

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 6x4 + 23x3 + 19x2 - 8x - 4

Chapter: Problem: 3.4.33

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. x4 - 4x3 + 5x2 - 4x + 4 = 0

Chapter: Problem: 3.1.33

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = x4 - 10x3 + 2, c = 3

Chapter: Problem: 3.5.33

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1 x2 + 2x - 3

Chapter: Problem: 3.2.33

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (x - 1)(x + 1)(x - 3)

Chapter: Problem: 33

College Algebra 7
In Exercises 33 to 36, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x3 + 3x2 + x + 3

Chapter: Problem: 3.3.34

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 2x3 + 9x2 - 2x - 9

Chapter: Problem: 3.4.34

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. x4 + 4x3 + 8x2 + 16x + 16 = 0

Chapter: Problem: 3.1.34

College Algebra 7
In Exercises 25 to 34, use synthetic division and the Remainder Theorem to find P(c). P(x) = x5 + 20x2 - 1, c = -4

Chapter: Problem: 3.5.34

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1 x2 - 2x - 8

Chapter: Problem: 3.2.34

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (x + 2)(x - 6)2

Chapter: Problem: 34

College Algebra 7
In Exercises 33 to 36, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x4 - 6x3 - 5x2 + 74x - 120

Chapter: Problem: 3.3.35

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 4x4 - 12x3 - 3x2 + 12x - 7

Chapter: Problem: 3.4.35

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. x4 + 4x3 - 2x2 - 12x + 9 = 0

Chapter: Problem: 3.1.35

College Algebra 7
In Exercises 35 to 44, use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x) = x3 + 2x2 - 5x - 6, x - 2

Chapter: Problem: 3.5.35

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x2 x2 + 4x + 4

Chapter: Problem: 3.2.35

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = -(x - 3)2 (x - 7)5

Chapter: Problem: 35

College Algebra 7
In Exercises 33 to 36, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x4 - x - 1

Chapter: Problem: 3.3.36

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x5 - x4 - 7x3 + 7x2 - 12x - 12

Chapter: Problem: 3.4.36

College Algebra 7
In Exercises 29 to 36, use a graph and your knowledge of the zeros of polynomial functions to determine the exact values of all the solutions of each equation. x4 + 3x3 - 6x2 - 28x - 24 = 0

Chapter: Problem: 3.1.36

College Algebra 7
In Exercises 35 to 44, use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x) = x3 + 4x2 - 27x - 90, x + 6

Chapter: Problem: 3.5.36

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 2x2 x2 - 1

Chapter: Problem: 3.2.36

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (x + 2)3 (x - 6)10

Chapter: Problem: 36

College Algebra 7
In Exercises 33 to 36, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x5 - 4x4 + 2x3 - x2 + x - 8

Chapter: Problem: 3.3.37

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x5 - 32

Chapter: Problem: 3.4.37

College Algebra 7
In Exercises 37 to 46, find a polynomial function of lowest degree with integer coefficients that has the given zeros. 4, -3, 2

Chapter: Problem: 3.1.37

College Algebra 7
In Exercises 35 to 44, use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x) = 2x3 + x2 - 3x - 1, x + 1

Chapter: Problem: 3.5.37

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 10 x2 + 2

Chapter: Problem: 3.2.37

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (2x - 3)4 (x - 1)15

Chapter: Problem: 37

College Algebra 7
In Exercises 37 to 42, find the zeros of the polynomial function. P(x) = x3 + 6x2 + 3x - 10

Chapter: Problem: 3.3.38

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = x4 - 1

Chapter: Problem: 3.4.38

College Algebra 7
In Exercises 37 to 46, find a polynomial function of lowest degree with integer coefficients that has the given zeros. -1, 1, -5

Chapter: Problem: 3.1.38

College Algebra 7
In Exercises 35 to 44, use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x) = 3x3 + 4x2 - 27x - 36, x - 4

Chapter: Problem: 3.5.38

College Algebra 7
In Exercises 21 to 42, determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = x2 x2 - 6x + 9

Chapter: Problem: 3.2.38

College Algebra 7
In Exercises 33 to 40, determine the x-intercepts of the graph of P. For each x-intercept, use the Even and Odd Powers of Theorem to determine whether the graph of P crosses the x-axis or intersects but does not cross the x-axis. P(x) = (5x + 10)6 (x - 2.7)5

Chapter: Problem: 38

College Algebra 7
In Exercises 37 to 42, find the zeros of the polynomial function. P(x) = x3 - 10x2 + 31x - 30

Chapter: Problem: 3.3.39

College Algebra 7
In Exercises 29 to 42, use Descartes Rule of Signs to state the number of possible positive and negative real zeros of each polynomial function. P(x) = 10x6 - 9x5 - 14x4 - 8x3 - 18x2 + x + 6

Chapter: Problem: 3.4.39

College Algebra 7
In Exercises 37 to 46, find a polynomial function of lowest degree with integer coefficients that has the given zeros. 3, 2i, -2i

Chapter: Problem: 3.1.39

College Algebra 7
In Exercises 35 to 44, use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of P(x). P(x) = x4 - 25x2 + 144, x + 3

Chapter: Problem: 3.5.39

College Algebra 7
In Exercises 21 to 42, determine the vertical and horiz