Synthethic division is commonly taught, but I have never actually had a proof/explanation shown to me. Why does it work?
Work So Far
I related the "$x$" to powers to 10, and then proceeded to relate synthetic division to non-polynomial division, but couldn't seem to find the correlation.
Research So Far
My teacher doesn't seem to have a valid explanation for why it works. A google search doesn't provide any good results either. All I seem to get is a Yahoo answers link with a badly formatted proof that makes it hard to understand and a physics forum link that links synthetic division to "normal division" by relating the "x" to 10, a conclusion I have already arrived at.