Use the rational roots theorem. The possible rational roots are:
Use synthetic division to start testing for rational zeros. If you need a refresher on synthetic division, see http://www.purplemath.com/modules/synthdiv.htm
All of the zeros of this function are, in fact, rational. Once you have found the first zero, the quotient of your synthetic division will be the coefficients of the 3rd degree polynomial factor. Apply the rational roots theorem and start checking more roots into the quotient polynomial. Note that if you tried and failed with a potential root when you were doing the 4th degree division, you can forget about that number when doing the 3rd degree polynomial.
Once you have found the second root, you will have a quadratic equation that can be easily factored to get the remaining two roots.
