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Math Help - factor theorm

  1. #1
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    factor theorm

    Given that x-1 and x+2 are factors of f(x)= x^3 + px + q where p and q are integers, find p and q.

    How do i start in find p and q????
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  2. #2
    Super Member Quacky's Avatar
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    Re: factor theorm

    If x-a is a factor, then f(a)=0
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  3. #3
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    Re: factor theorm

    so wait if i use x-1 then where x is, it would be replaced by 1,

    F(1) = 1^3 + p(1) + q

    and i was just end up where i started, so how to advance on this questions , and thanks
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  4. #4
    Super Member Quacky's Avatar
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    Re: factor theorm

    F(1) = 1^3 + p(1) + q = 0
    This gives you one equation in p and q. Now find another using the other factor.
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  5. #5
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    Re: factor theorm

    then i simultaneously solve right???
    thanks alot your help greatly appreciated,
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: factor theorm

    Another method:

    x^3+px+q=(x-1)(x+2)(x-k)

    We know k is real as complex roots come in conjugate pairs.

    x^3+px+q=\left(x^2+x-2\right)(x-k)

    x^3+px+q=\left(x^3+x^2-2x\right)-\left(kx^2+kx-2k\right)

    x^3+0\cdot x^2+px+q=x^3+(1-k)x^2-(2+k)x+2k

    Now equate coefficients.
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