I recently put together a calculator to perform synthetic division for a polynomial of maximum degree of 6 or less divided by (x - c) where c is a constant that the user enters.
Located on the algebra page, and searchable by synthetic, division, quotient, polynomial, this calculator will show you each step in the synthetic division process. It provides the quotient answer including a remainder amount if applicable. I've done some moderate testing of this program. Please let me know if anybody wants enhancements, or sees corrections that can be made. Calculator instructions are located inside the link at the top of the page.
For the math work section, I wanted to follow how they do it on Wikipedia here ---> Ruffini's rule - Wikipedia, the free encyclopedia
The calculator is located here, enjoy: