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Math Help - factorising cubics

  1. #1
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    factorising cubics

    is there any formula or neat trick to factorise a cubic equation like

    x^3 + 4x^2 -28x + 32=0?
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  2. #2
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    Quote Originally Posted by Tekken View Post
    is there any formula or neat trick to factorise a cubic equation like

    x^3 + 4x^2 -28x + 32=0?
    Yes, use the factor and remainder theorems.

    For any polynomial P(x), if P(a) = 0 then x - a is a factor.

    The factors of 32 are \pm 1, \pm 2, \pm 4, \pm 8, \pm 16, \pm 32.

    So try substituting these values into the expression.
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  3. #3
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    That will allow you to find any factors with rational coefficients. More generally, you could use Cardano's cubic formula to find a solution, x_0, then divide by x- x_0 to reduce the problem to factoring a quadratic.
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