54. f(x) = x4 - 3x3 – x² – 12x - 20 part (a) all real %3D (Hint: One factor is x2 + 4.) OsEO Finding the Zeros of a Polynomial Function In Exercises 55-60, use the given zero to find all the zeros of the function. Function Zero 55. f(x) = x3 -x2 + 4x - 4 56. f(x) 2i $7-40, phing ros in ne all = 2x3 + 3x2 + 18x + 27 57. g(x) = x³ – 8x² + 25x - 26 58. g(x) = x3 + 9x² + 25x + 17 3i %3D 3 + 2i -4 + i 59. h(x) = x4 – 6x3 + 14x² – 18x + 9 %3D 1- /2i -2+ 3i 60. h(x) = x4 + x³ – 3x² – 13x + 14 Finding the Zeros of a Polynomial Function In Exercises 61-72, write the polynomial as the product of linear factors and list all the zeros of the function. 61. f(x) = x² + 36 ith 1 a 62. f(x) = x² + 49 63. h(x) = x² – 2x + 17 64. g(x) = x² + 10x + 17 nts 65. f(x) = x4 – 16 66. f(y) = y4 – 256 ny 67. f(z) = z2 - 2z + 2 %3D 68. h(x) = x3 - 3x2 + 4x - 2 69. g(x) = x3 - 3x2 + x + 5 70. f(x) = x³ – x² + x + 39 %3D 71. g(x) = x4 – 4x3 + 8x² - 16x + 16 %3D 72. h(x) = x4 + 6x3 + 10x2 + 6x + 9 A Finding the Zeros of a Polynomial Function In Exercises 73-78, find ali the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. 73. f(x) = x³ + 24x² + 214x + 740 5s2 + 5 562 12s – 263
54. f(x) = x4 - 3x3 – x² – 12x - 20 part (a) all real %3D (Hint: One factor is x2 + 4.) OsEO Finding the Zeros of a Polynomial Function In Exercises 55-60, use the given zero to find all the zeros of the function. Function Zero 55. f(x) = x3 -x2 + 4x - 4 56. f(x) 2i $7-40, phing ros in ne all = 2x3 + 3x2 + 18x + 27 57. g(x) = x³ – 8x² + 25x - 26 58. g(x) = x3 + 9x² + 25x + 17 3i %3D 3 + 2i -4 + i 59. h(x) = x4 – 6x3 + 14x² – 18x + 9 %3D 1- /2i -2+ 3i 60. h(x) = x4 + x³ – 3x² – 13x + 14 Finding the Zeros of a Polynomial Function In Exercises 61-72, write the polynomial as the product of linear factors and list all the zeros of the function. 61. f(x) = x² + 36 ith 1 a 62. f(x) = x² + 49 63. h(x) = x² – 2x + 17 64. g(x) = x² + 10x + 17 nts 65. f(x) = x4 – 16 66. f(y) = y4 – 256 ny 67. f(z) = z2 - 2z + 2 %3D 68. h(x) = x3 - 3x2 + 4x - 2 69. g(x) = x3 - 3x2 + x + 5 70. f(x) = x³ – x² + x + 39 %3D 71. g(x) = x4 – 4x3 + 8x² - 16x + 16 %3D 72. h(x) = x4 + 6x3 + 10x2 + 6x + 9 A Finding the Zeros of a Polynomial Function In Exercises 73-78, find ali the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. 73. f(x) = x³ + 24x² + 214x + 740 5s2 + 5 562 12s – 263
Chapter3: Polynomial Functions
Section3.2: Polynomial Functions Of Higher Degree
Problem 43E: In Exercises 33-48, (a) find all real zeros of the polynomial function, (b) determine whether the...
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Transcribed Image Text:54. f(x) = x4 - 3x3 – x² – 12x - 20
part (a)
all real
%3D
(Hint: One factor is x2 + 4.)
OsEO
Finding the Zeros of a Polynomial
Function In Exercises 55-60, use the given
zero to find all the zeros of the function.
Function
Zero
55. f(x) = x3 -x2 + 4x - 4
56. f(x)
2i
$7-40,
phing
ros in
ne all
= 2x3 + 3x2 + 18x + 27
57. g(x) = x³ – 8x² + 25x - 26
58. g(x) = x3 + 9x² + 25x + 17
3i
%3D
3 + 2i
-4 + i
59. h(x) = x4 – 6x3 + 14x² – 18x + 9
%3D
1- /2i
-2+ 3i
60. h(x) = x4 + x³ – 3x² – 13x + 14
Finding the Zeros of a Polynomial
Function In Exercises 61-72, write the
polynomial as the product of linear factors
and list all the zeros of the function.
61. f(x) = x² + 36
ith
1 a
62. f(x) = x² + 49
63. h(x) = x² – 2x + 17
64. g(x) = x² + 10x + 17
nts
65. f(x) = x4 – 16
66. f(y) = y4 – 256
ny
67. f(z) = z2 - 2z + 2
%3D
68. h(x) = x3 - 3x2 + 4x - 2
69. g(x) = x3 - 3x2 + x + 5
70. f(x) = x³ – x² + x + 39
%3D
71. g(x) = x4 – 4x3 + 8x² - 16x + 16
%3D
72. h(x) = x4 + 6x3 + 10x2 + 6x + 9
A Finding the Zeros of a Polynomial Function In
Exercises 73-78, find ali the zeros of the function. When
there is an extended list of possible rational zeros, use
a graphing utility to graph the function in order to
disregard any of the possible rational zeros that are
obviously not zeros of the function.
73. f(x) = x³ + 24x² + 214x + 740
5s2 + 5
562
12s –
263
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