Lial - College Algebra 13th Edition

Ch. 3 - Polynomial and Rational Functions

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Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

Section 3.3

Problem 67

Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. 2-i, 3, and -1

Problem 73

Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. 2-i and 6-3i

Problem 79

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 2 x^{3} - 4 x^{2} + 2 x + 7$

Problem 81

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 4 x^{3} - x^{2} + 2 x - 7$

Problem 82

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 3 x^{3} + 6 x^{2} + x + 7$

Problem 83

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 5 x^{4} + 3 x^{2} + 2 x - 9$

Problem 84

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 3 x^{4} + 2 x^{3} - 8 x^{2} - 10 x - 1$

Problem 85

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = - 8 x^{4} + 3 x^{3} - 6 x^{2} + 5 x - 7$

Problem 86

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 6 x^{4} + 2 x^{3} + 9 x^{2} + x + 5$

Problem 87

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = x^{5} + 3 x^{4} - x^{3} + 2 x + 3$

Problem 88

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 2 x^{5} - x^{4} + x^{3} - x^{2} + x + 5$

Problem 89

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 2 x^{5} - 7 x^{3} + 6 x + 8$

Problem 91

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 5 x^{6} - 6 x^{5} + 7 x^{3} - 4 x^{2} + x + 2$

Problem 93

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = 7 x^{5} + 6 x^{4} + 2 x^{3} + 9 x^{2} + x + 5$

Problem 94

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $ƒ (x) = - 2 x^{5} + 10 x^{4} - 6 x^{3} + 8 x^{2} - x + 1$

Problem 97

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary. $ƒ (x) = x^{4} + x^{3} - 9 x^{2} + 11 x - 4$

Problem 99

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary. $ƒ (x) = 2 x^{5} + 11 x^{4} + 16 x^{3} + 15 x^{2} + 36 x$

Problem 103

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary. $ƒ (x) = 2 x^{4} - x^{3} + 7 x^{2} - 4 x - 4$

Section 3.4

Problem 9

Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=2x⁴

Problem 18

Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=(1/3)(x+3)⁴-3

Problem 19

Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=(1/2)(x-2)²+4

Problem 21

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=5x⁵+2x³-3x+4

Problem 22

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=-x³-4x²+2x-1

Problem 24

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=4x⁷-x⁵+x³-1

Problem 25

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=9x⁶-3x⁴+x²-2

Problem 26

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=10x⁶-x⁵+2x-2

Problem 27

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=3+2x-4x²-5x¹⁰

Problem 28

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=7+2x-5x²-10x⁴

Problem 31

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-2x(x-3)(x+2)

Problem 32

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=-x(x+1)(x-1)