Math 11010
Spring 2011
Assignment 4: Sections 3.1-3.3
Name___________________________________
DUE: Thursday, March 10
Directions: Choose the one alternative that best completes the statement or answers the question. Fill-in the Scantron
with your final answer. Show all work/steps on separate paper(s).
SECTION 3.1
Find the correct end behavior diagram for the given polynomial function.
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1) f(x) = - x3 + 5x2 + 9x - 9
3
A)
2) f(x) = 3.74x4 + 3x2 + x - 8
A)
B)
C)
D)
B)
C)
D)
3) f(x) = -x6 + 8x5 - x2 - 7x + 5
A)
B)
4) f(x) = 6x3 + 2x2 - 2x + 5
A)
1)
C)
B)
C)
D)
D)
Use substitution to determine whether the given number is a zero of the given polynomial.
5) -3; f(x) = -8x3 - 8x2 + x - 141
A) Yes
B) No
6) 2; f(x) = x4 - 6x2 + 8
A) Yes
B) No
Find the zeros of the polynomial function and state the multiplicity of each.
7) f(x) = -5x2 (x - 9)(x + 3)3
A) -3, multiplicity 3; 0, multiplicity 2; 9, multiplicity 1
B) -3, multiplicity 1; 3, multiplicity 1; 9, multiplicity 1
C) -3, multiplicity 3; 0, multiplicity 2; 3, multiplicity 1; 9, multiplicity 1
D) -3, multiplicity 3; 9, multiplicity 1
2)
3)
4)
5)
6)
7)
8) f(x) = x4 - 20x2 + 64
A) 16, multiplicity 2; 4, multiplicity 2
B) 16, multiplicity 1; 4, multiplicity 1
C) -4, multiplicity 1; 4, multiplicity 1; -2, multiplicity 1; 2, multiplicity 1
D) 16, multiplicity 2; 2, multiplicity 1
8)
9) f(x) = x3 + x2 - 5x - 5
A) -1, multiplicity 1; 1, multiplicity 1; 5, multiplicity 1
B) -1, multiplicity 1; 1, multiplicity 1; 5, multiplicity 1; - 5, multiplicity 1
C) -1, multiplicity 1; 1, multiplicity 1; 5, multiplicity 1
D) -1, multiplicity 1; 5, multiplicity 1; - 5, multiplicity 1
9)
1
SECTION 3.2
For the function find the maximum number of real zeros that the function can have, the maximum number of x-intercepts
that the function can have, and the maximum number of turning points that the graph of the function can have.
10) f(x) = 7x3 + 4x2 - 3x + 3
10)
A) 2; 2; 1
B) 3; 3; 3
C) 3; 2; 1
D) 3; 3; 2
11) f(x) = -x6 + 8x5 - x2 - 6x + 4
A) 6; 6; 5
B) 6; 5; 5
C) 5; 5; 6
D) 6; 6; 6
12) g(x) = -x5 - 8x3 - 3x + 5
A) 5; 5; 4
C) 5; 5; 5
D) 5; 4; 3
B) 5; 4; 4
Graph the function.
13) f(x) = 2x(x + 1)(x + 2)
11)
12)
13)
A)
B)
2
C)
D)
14) f(x) = x 4 - 6x3 + 8x2
14)
A)
B)
3
C)
D)
15) f(x) = -x4 - 4x2
15)
A)
B)
4
C)
D)
16) f(x) = 2x3 - 4x2 - 2x + 4
16)
A)
B)
5
C)
D)
SECTION 3.3
Use long division to determine whether the binomial is a factor of f(x).
17) f(x) = x 4 - x3 - 3x 2 + 4x + 7; x + 2
A) No
B) Yes
18) f(x) = 4x3 - 23x2 + 5x + 50; x - 5
A) Yes
B) No
17)
18)
A polynomial P(x) and a divisor d(x) are given. Use long division to find the quotient Q(x) and the remainder R(x) when
P(x) is divided by d(x), and express P(x) in the form d(x)· Q(x) + R(x).
19) P(x) = x3 - x2 + 7
19)
d(x) = x + 2
A) (x + 2)(x2 - 3x + 6) + 7
C) (x + 2)(3x2 - 4x + 2) + 19
B) (x + 2)(x2 + x + 2) + 11
D) (x + 2)(x2 - 3x + 6) - 5
20) P(x) = 2x4 - x3 - 15x2 + 3x
d(x) = x + 3
A) (x + 3)(2x3 + 5x2 + 3) + 9
20)
B) (x + 3)(2x3 - 7x2 + 6x - 15) - 45
D) (x + 3)(2x3 - 5x2 + 3) + 9
C) (x + 3)(2x3 - 7x2 + 6x - 15) + 45
21) P(x) = x3 - 4
d(x) = x + 4
21)
A) (x + 4)(x2 + 4x + 16) + 8
C) (x + 4)(x2 + 4x + 16) + 0
B) (x + 4)(x2 - 4x + 16) - 68
D) (x + 4)(x2 - 4x + 16)
Use synthetic division to find the quotient and the remainder.
22) (2x3 + 3x2 + 4x - 10) ÷ (x + 1)
A) Q(x) = (2x2 + x + 3); R(x) = -13
B) Q(x) = (2x2 + 5x + 9); R(x) = -1
C) Q(x) = (2x2 + 5x + 9); R(x) = 1
D) Q(x) = (2x2 + x + 3); R(x) = 13
6
22)
23) (2x4 - x3 - 15x2 + 3x) ÷ (x + 3)
A) Q(x) = (2x3 + 5x2 + 3); R(x) = 9
C) Q(x) = (2x3 - 5x2 + 3); R(x) = 9
B) Q(x) = (2x3 - 7x2 + 6x - 15); R(x) = - 45
D) Q(x) = (2x3 - 7x2 + 6x - 15); R(x) = 45
Use synthetic division to find the function value.
24) f(x) = x 5 - 10x4 + 17x3 - 2x - 300; find f(3).
A) -412
B) -414
C) 186
D) -416
25) f(x) = x 3 + 2x2 + 5x - 3; find f(-3)
A) -21
B) -27
C) 30
D) 27
Using synthetic division, determine whether the numbers are zeros of the polynomial.
26) 2, -5; f(x) = x3 - 4x2 - 31x + 70
A) Yes; no
B) No; yes
C) Yes; yes
D) No; no
27) 7, 3; f(x) = x3 - 11x2 + 36x - 36
A) No; yes
B) No; no
C) Yes; no
D) Yes; yes
28) i, -i, 4; f(x) = x3 - 3x2 + x - 3
A) No; no; no
B) No; no; yes
C) Yes; yes; no
D) Yes; no; no
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23)
24)
25)
26)
27)
28)