Division of polynomials is actually kind of fun, according to my tutoring students; it's easy to get the hang of, and it reminds you of primary school when you didn't have so much homework! The main uses of these two are finding slant asymptotes of rational functions and finding the roots of polynomials (not that you'd ever want to do either of those things). In these videos I emphasize the common mistake I see most: not putting in a zero term when a power is missing. (That advice doesn't make sense to you? You should watch these videos!)
Polynomial Long Division
In this video I cover how to divide polynomials the same way you would have divided 14 into 159 in grammar school. The long way. Want to divide x3-1 into 5x5-3x4+3x-1? You came to the right place.
In this one we get to a shortcut technique for dividing polynomials: synthetic division. This shortcut only works for dividing in factors with an exponent of 1, such as "x-2" or "x+6", but that's what you usually have to do in this class. Yay! Synthetic division is also used for the Remainder Theorem.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)