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Thread: 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 $\displaystyle P(x)$, if $\displaystyle P(a) = 0$ then $\displaystyle x - a$ is a factor.

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

    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, $\displaystyle x_0$, then divide by $\displaystyle x- x_0$ to reduce the problem to factoring a quadratic.
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