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The function f(x)=ax^3-x^3+bx-24 has three factors. Two of these factors are x-2 and x+4. Determine the values of a and b , and then determine the other factor

  • math -

    synthetic division yields remainders

    f(x) = (x-2)*p(x) + 8a+2b-28
    f(x) = (x+4)*q(x) + (-64a-4b-40)

    so,
    8a+2b = 28
    64a+4b = -40

    a = -2
    b = 22

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

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