SOLUTION: How can I factor X^3 � 13x +12 without trial and error? Thanks!

Question 832975: How can I factor X^3 � 13x +12 without trial and error?
Thanks!

Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
That one is to the power of three? Use Rational Roots Theorem, and check for roots: -1, -2, -3, -4, -6, -12, 1, 2, 3, 4, 6, 12...
Only three of them at most, will work as roots.

Any trouble, then tell.

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NOTE: I tried -1, and 1 first, and found 1 is a root, for the binomial factor of (x-1).
This resulted in as the quotient from the synthetic division. That quadratic factor has roots -4 and +3, using general solution to a quadratic equation, so the binomial factors are (x+4) and (x-3).
The Factorization of your given expression is
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