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College algebra

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Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=x^3-2x^2-13x-10
x=

  • College algebra -

    f(1) = 1-2-13-10 ≠ 0
    f(-1) = -1 - 2 + 13 -10 = 0 , so x+1 is a factor

    by synthetic division
    x^3 - 2x^2 - 13x - 10 = (x+1)(x^2 - 3x - 10)
    = (x+1)(x-5)(x+2) = 0 for roots

    x = -1 or x = -2 or x = 5

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