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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