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Name _____________________________
Date ___________________

Polynomials
(Answer ID # 0838127)
Complete.
1.   (-2x3 - 2x2 + 12x)  ÷  (x + 3)
2.   (3x3 - 15x2 - 42x)  ÷  (x + 2)
3.   (-2x3 - 38x2 - 180x)  ÷  (x + 10)

Complete.
4.   (x4 + 8x3 - 18x2 - 72x + 81)  ÷  (x2 + 8x - 9)
5.   (-6x4 - 2x3 + x2 + 72x + 55)  ÷  (-x2 - 2x - 5)
6.   (x4 - 12x3 - 14x2 + 132x + 33)  ÷  (x2 - 12x - 3)

Describe the left and right behavior of the graph of the function.
7.   f(x) = 8x - x6 + 2x2 - 3x3 + x7 - 6x5
8.   f(x) = -5x5 + x4 - 9x3 + 3x2 - 3
9.   f(x) = -6x6 - 2x5 + 7x4 - x3 - 3x2 + 2x - 5

Graph each function. State the points of any local maxima or minima to the nearest tenth.
10.   f(x) = 3x3 - 6x + 20
11.   f(x) = x3 - 4x2 - 4x - 12
12.   f(x) = x3 + 5x2 + x - 3

 

Factor.
13.   f(x) = -2x3 - 6x2 - 4x
14.   f(x) = x3 + 4x2 - 31x - 70
15.   f(x) = x3 - 343

Factor.
16.   f(x) = 2x3 - 30x2 + 112x
17.   f(x) = -2x3 - 2x2 + 4x
18.   f(x) = x3 - 1000

What is the missing factor?
19.   f(x) = x3 - 8  
= ( ? )(x2 + 2x + 4)
20.   f(x) = -3x3 + 72x2 - 432x  
= ( ? )(x - 12)(-3x)
21.   f(x) = x3 - 64  
= ( ? )(x2 + 4x + 16)

Factor.
22.   f(x) = x3 + 8x2 - 10x - 80
23.   f(x) = -4x3 + 4x2 + 440x
24.   f(x) = x3 - 12x2 + 20x

 

Is the given expression a factor of the polynomial?
25.   f(x) = -x3 - 3x2 + 54x  
Is x - 6 a factor?
26.   f(x) = x3 - 1728  
Is x - 15 a factor?
27.   f(x) = x3 - 5x2 - 46x - 40  
Is x + 1 a factor?

Factor. One factor is given.
28.   f(x) = 4x3 + 48x2 + 44x
Factor: 4x
29.   f(x) = 8x3 - 1728
Factor: 4x2 + 24x + 144
30.   f(x) = x3 + 2x2 - 8x
Factor: x - 2

Complete
31.   f(x) = -4x3 - 24x2 + 64x  
Is x - 2 a factor?
32.   What is the missing factor?
f(x) = 4x3 - 84x2 + 440x  
= ( ? )(x - 10)(4x)
33.   Factor.
f(x) = -2x3 - 10x2 + 132x

Factor and solve.
34.   f(x) = -3x3 + 54x2 - 243x
35.   f(x) = x3 - 7x2 - 7x + 49
36.   f(x) = 27x3 + 216

 

Factor and solve.
37.   f(x) = -3x3 + 18x2 - 15x
38.   f(x) = x3 + 23x2 + 156x + 288
39.   f(x) = x3 - 3x2 - 6x + 18

Factor and solve.
40.   f(x) = x3 + 8
41.   f(x) = -4x3 + 44x2 - 112x
42.   f(x) = x3 + 8x2 - 8x - 64

Apply variable substitution and then factor to find all of the roots.
43.   f(x) = x3 - 49x + 120
44.   f(x) = 8x3 - 512
45.   f(x) = x3 + 729

State all possible rational zeros.
46.   f(x) = x3 - 4x2 - 4x + 16
47.   f(x) = 5x4 + 8x3 - 18x2 - 32x - 8
48.   f(x) = 10x4 - 7x3 - 11x2 + 7x + 1

 

Find all the rational zeros.
49.   f(x) = x4 + 8x2 - 9
50.   f(x) = 4x4 + 7x3 - 25x2 - 35x + 25
51.   f(x) = 3x3 + 18x2 - 21x

Find all zeros.
52.   f(x) = x4 - 2x3 - 6x2 + 10x - 3
53.   f(x) = -3x3 + 21x2 - 18x
54.   f(x) = x3 - 5x2 + x + 15

State all possible rational zeros.
55.   f(x) = 11x4 + 41x3 + 44x2 + 10x - 4
56.   f(x) = x4 - 3x3 - 2x2 + 12x - 8
57.   f(x) = x3 - 6x2 + 9x

Find all the rational zeros.
58.   f(x) = x3 - x2 + 25x - 25
59.   f(x) = 9x4 + 6x3 - 20x2 - 6x + 11
60.   f(x) = 3x3 - 2x2 - 9x + 2

 

Find all zeros.
61.   f(x) = 8x4 - 7x3 - 19x2 + 7x + 11
62.   f(x) = x3 + 7x2 + x + 7
63.   f(x) = x3 - 8x2 + 17x - 10

 

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