## Precalculus Supplement: Synthetic Division

I think it is a sign.

In the question How does Synthetic Division Work? by the user Riddler on math.stackexchange, Riddler says that he’s never seen a proof of Synthetic Division. This gave me a great case of Mom’s Corollary (the generalization of the fact that when mothers tell you something, you are often reminded of specific cases of it within three days – at least with my mom), as it came up with a student whom I’m tutoring. It turns out many of my students haven’t liked synthetic division. I chatted with some of the other Brown grads, and in general, they didn’t like synthetic division either.

It was one of those things that was taught to us before we thought about why different things worked. Somehow, it wasn’t interesting or useful enough to be revisited. But let’s take a look at synthetic division after the fold: