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Sample edHelper.com - Polynomials Worksheet

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Polynomials
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 + 44xFactor: 4x
 29 f(x) = 8x3 - 1728Factor: 4x2 + 24x + 144
 30 f(x) = x3 + 2x2 - 8xFactor: 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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