Id start out by finding a zero on my cacluator. For example, 2 is a zero in that function. And, then Id do synthetic division to make it quadratic and then factor it. Are you familier with synthetic division?
There are many approaches to solving polynomials of a high degree. Synthetic division is probably the best one. Lets call the leading coefficient of an n degree polynomial Q and lets call the last term of the same polynomial P. Now, calculate all the values of P/Q and use synthetic division, with those values (only those values could possibly work). Have you heard of Descarte's Rule of Signs? It gives you some direction as to where the roots might be.
Descartes' Rule of Signs