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.
As many examples as needed to practice may be generated.
Step by step solution