Students will learn what a polynomial's reciprocal polynomial is. Then students will learn the following theorem: \(a\) is a root of a polynomial \(p\) if and only if \(1/a\) is a root of the reciprocal polynomial of \(p.\) This will be demonstrated for at least one quadratic, and at least one cubic. Next, students will learn what palindromic polynomials are, and how to use our new theorem to factor them. Finally, students will see a proof of the theorem for quadratic polynomials, which generalizes to polynomials of any degree. Here's a video on all that.
Note: This topic is not covered by Khan Academy.