First apply the Rational Root Theorem. The possible rational roots of:
are any rational number of the form
where and is a factor of and and is a factor of
Your lead coefficient being 1 simplifies things a little...your possible rational roots are:
Use Synthetic Division and the Remainder Theorem to determine if any of these 8 possibilities are actually roots of the given equation.
If you are unfamiliar with the process of synthetic division, check out Purple Math's explanation at http://www.purplemath.com/modules/synthdiv.htm.
The Remainder Theorem says that the remainder when you use synthetic division with a divisor of is equal to , and if , then must be a root of
Fortunately for this particular problem, one of the rational roots actually works. When you find the correct synthetic divisor, you will be left with the coefficients of a quadratic equation that can be solved with the quadratic formula to yield a conjugate pair of complex roots.
