Synthetic Division
Dividing polynomials by linear terms via the tableau method of synthetic division used to be a standard part of the high-school mathematics curriculum. It is not part of the Common Core, but many States, in rewriting their own standards, have put it back in. I have no objections to teaching any piece of mathematics if it is taught with thinking, context, and meaning.
This video, for teachers who have thought about and struggled with teaching this topic, is my (very swift) attempt to give a meaningful and honest context for it.