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pre-calculus

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find the complex zeros of the polynomial function. write F in the factored form. f(X)=x^3-7x^2+20x-24

use the complex zeros to write f in factored form.
f(x)=
(reduce fractions and simplify roots)

  • pre-calculus - ,

    try factors of 24
    f(1) = 1 - 7 + 20 - 24 ≠0
    f(-1) = -1 -7 - 20 - 24 ≠ 0
    f(2) = ≠0
    f(-2) ≠ 0
    f(3) = 27 - 63 + 60 - 24 = 0
    So (x-3) is a factor

    Using synthetic division, I got
    x^3-7x^2+20x-24 = (x-3)(x^2 -4x + 8)

    Solving the 2nd part:
    x^2 - 4x + .... = -8 + ....
    x^2 - 4x + 4 = -8+4
    (x-2)^2 = -4
    x-2 = ± 2i
    x = 2 ± 2i

    f(x) = (x-3)(x^2 -4x + 8)

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