This site from the Richland Community College contains information on long and synthetic division, the remainder theorem and the factor theorem.

Synthetic division is thoroughly explained using long division as a starting point. The examples are very detailed and provide the steps necessary for completing the process of synthetic division.

This article gives an overview for adding, subtracting, multiplying, and dividing polynomials. Examples are given, but more importantly, they are accompanied with explanations of why the process worked.