Factor a Polynomial Using Rational Root and Factor theorems

The rational root theorem and the factor theorem are used, in steps, to factor completely a cubic polynomial.

Rational root theorem: If the polynomial P of degree 3 (or any other polynomial), shown below, has rational zeros equal to p/q, then p is a integer factor of the constant term d and q is an integer factor of the leading coefficient a.

P(x) = a x
3 + b x 2 + c x + d

Factor theorem: x - r is a factor of polynomial P(x) if and only if P(r) = 0.

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