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Math Help - Algebra II

  1. #1
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    Algebra II

    Find the number a such that x-1 is a factor of x^3+ax^2-x+8
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  2. #2
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    Re: Algebra II

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  3. #3
    Junior Member PaulAdrienMauriceDirac's Avatar
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    Re: Algebra II

    Also, you could use Vieta's theorem.

    When you have: P(x)=x^3+px+qx+r, you know that:

    x_1+x_2+x_3=-p

    x_1x_2+x_1x_3+x_2x_3=q

    x_1x_2x_3=-r

    ... where x_1,x_2,x_3 are roots of P(x).

    So when you have P(x)=x^3+ax^2-x+8 and you know that 1 is root ( x_1=1), you can write three equations:

    1+x_2+x_3=-a

    x_2+x_3+x_2x_3=-1

    x_2x_3=-8

    ... so you have 3 equations with three unknowns, and you can solve for a.
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  4. #4
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    Re: Algebra II

    Well, if you really want to do it the hard way! Personally I would prefer to evaluate the polynomial at x= 1.
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  5. #5
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    Re: Algebra II

    Thanks guys that was a huge help!!
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