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31 August, 00:50

1. Consider the function f (x) = 5x^3 - 31x^2 - 129x + 27

a) verify that f (9) = 0. Since f (9) = 0, what is the factor?

b) find the remaining two factors

c) state all three zeros of the function

2. Use the factor theorem to determine if 3x - 4 is a factor of f (x) = 3x^2 + 2x - 8

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Answers (1)
  1. 31 August, 01:02
    0
    The answer to your question is below

    Step-by-step explanation:

    Data

    1. - f (x) = 5x³ - 31x² - 129x + 27

    a) f (9) = 5 (9) ³ - 31 (9) ² - 129 (9) + 27

    f (9) = 5 (729) - 31 (81) - 1161 + 27

    f (9) = 3645 - 2511 - 1161 + 27

    f (9) = 0

    b. - I will use synthetic division

    5 - 31 - 129 + 27 9

    45 126 - 27

    5 14 - 3 0

    Trinomial = 5x² + 14x - 3

    Factor 5x² + 15x - 1x - 3

    5x (x + 3) - 1 (x + 3)

    b) (x + 3) (5x - 1)

    x₂ + 3 = 0 5x₃ - 1 = 0

    x₂ = - 3 x₃ = 1/5

    c) The roots are x₁ = 9, x₂ = - 3 and x₃ = 1/5

    2. - f (x) = 3x² + 2x - 8 factor = 3x - 4

    x + 2

    3x - 4 3x² + 2x - 8

    -3x² + 4x

    0 + 6x - 8

    -6x + 8

    0 Remainder

    As the remainder was "0", 3x - 4 is a factor of 3x² + 2x - 8
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