Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Can you please do number 55
Transcribed Image Text:9. P(x) = -x³ - 2x + 6,
10. P(x) = x + 2r - 10x,
11. P(x) = 2x³ 3x² - 2x,
12. P(x) = 4x³ + 7x +9,
13. P(x) = 8x4 + 4x³ + 6x²,
14. P(x) = 27x59x² + 3x²-3,
310 CHAPTER 3 Polynomial and Rational Functions
9-14 Division of Polynomials Two polynomials P and D are
given. Use either synthetic or long division to divide P(x) by
D(x), and express P in the form
P(x) = D(x) Q(x) + R(x)
D(x) = x + 1
D(x) = x-3
D(x) = 2x - 3
D(x) = 2x + 1
D(x) = 2x² + 1
P(x) = 6x²
40x6 + 16x³ - 200x4
- 60 - 69x² + 13x – 139
uol pergah to Calculate P(7) by (a) using synthetic division and (b) sub
tuting x= 7 into the polynomial and evaluating directly.
53-56 Factor Theorem Use the Factor Theorem to show the
der Theorem to Find the Value
x-c is a factor of P(x) for the given value(s) of c.
-53. P(x)= x³ 3x² + 3x - 1,
c = 1
54. P(x) = x³ + 2x² - 3x - 10,
A songsb 10 21 55. P(x) = 2x³ + 7x² + 6x-5,
ona (d noils
25-38 Synthetic Division of Polynomials Find the quotient
and remainder using synthetic division.
2x²5x + 3
15-24 Long Division of Polynomials
remainder using long division.
x²-3x + 7
x-2
15.
35.
36.
37.
17.
19.
21.
23.
25.
33.
27.
29.
x² + 2x² + 2x + 1
x + 2
31, +³¹-8r+2
-
x + 3
x² + 3x³ - 6
x-1
2x² + 3x² - 2x + 1
4x³ + 2x² - 2x - 3
2x + 1
+³+ 2x + 1 bna.
x²-x+ 3
6x³ + 2x² + 22x (2
2x² + 5
+x²+x²+1
x² + 1
- 3
3x² + x
x + 1
2019 bei 16.
Inimonyfog
x-001 noled
x³ - 27
x - 3
6x + 10x³ + 5x² + x + 1
x + }
18.
20.
22.
24.
26.
28.
38.
30.
32.
34.
D(x) = 3x²-3x + 1
Find the quotient and
3x³-12x²9x + 1
x - 5
**-x³+x²-x+ 2
x-2
x³9x² + 27x27
x-3
alsimon lot to noiivid @ 8-8
x³ + 2x² = x + 1
x + 3
x³ + 3x² + 4x + 3
3x + 6
x²-3x³ + x2
rẻ -5x+1
9x² - x + 5
3x² - 7x
2x³-7x4-13
4x² - 6x + 8.
c = -1
-x²+x-4 = (x)Q
*+1 bizob od led
4x²-3 mogaomoo 9
x-2
x 16
x + 2
39. P(x) = 4x² + 12x + 5,
40. P(x) = 2x² + 9x + 1, c= /
41. P(x)=x² + 3x² - 7x + 6₁ c = 2
39-51 Remainder Theorem Use synthetic division and the
Remainder Theorem to evaluate P(c).
42. P(x) = x¹-x² + x + 5₁ c = -1
43. P(x) = x² + 2x²2 - 7, c = -2
44. P(x) = 2x³ - 21x² + 9x 200, c = 11
45. P(x) = 5x + 30x³ 40x² + 36x + 14, c = -1
46. P(x) = 6x² + 10x³ + x + 1,
c = -2
47. P(x)=x²-3x² - 1, c = 3
48. P(x) = -2x + 7x³ + 40x4 - 7x² + 10x + 112, c=
49. P(x) = 3x³ + 4x² - 2x + 1,
c = 3
50. P(x) = x¹ - x + 1, c = 1
51. P(x) = x³ + 2x²-3x - 8, c = 0.1
52. Remainder Theorem Let
56. P(x) = x + 3x³ 16x² - 27x + 63, c = 3, -3
ei Isimon yloq Belesbision for this probl
57-62 Factor Theorem Show that the given value(s) of car
zeros of P(x), and find all other zeros of P(x).
57. P(x)= x³ + 2x²9x 18, c = -2
58. P(x) = x³ - 5x² - 2x + 10,
c=5
59. P(x)=x²-x² - 11x + 15,
c = 3
60. P(x) = 3x -x³-21x² - 11x + 6, c = -2,
61. P(x) = 3x - 8x³ - 14x² + 31x + 6, c = -2,3
62. P(x) = 2x13x³ + 7x² + 37x + 15, c = -1,3
63-66 Finding a Polynomial with Specified Zeros Find a
ied Zeros Find
polynomial of the specified degree that has the given zeros.
2111263. Degree 3; zeros -1, 1, 3
279300
64. Degree 4; zeros -2,0, 2, 4 laimonyjog od sbivib sw
c = 2
c = }
65. Degree 4; zeros -1, 1, 3, 5
66. Degree 5; zeros -2, -1, 0, 1, 2 viol
13AU
67-70 Polynomials with Specified Zeros Find a polynomial
of the specified degree that satisfies the given conditions.
67. Degree 4; zeros -2, 0, 1, 3; coefficient of x² is 4
68. Degree 4; zeros -1, 0, 2,; coefficient of x³ is 3
69. Degree 4; zeros -1, 1, V2; integer coefficients and
constant term 6 had
70. Degree 5; zeros -2, -1, 2, V5; integer coefficients and
constant term 40
SKILLS
71-74-
mial of t
71. Deg
-
73. De
C-
3.4
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