Polynomials, factoring, long division, rates of change & features of graphs

Polynomials can be difficult to factor, but with the integer or rational roots theorems, we can assess all possible roots and then do long division or synthetic division to find which possible values actually are roots. This video shows how to do that, but for higher order polynomials with leading coefficients and constants that are not 1, this process can be extremely time consuming. Hence, we should use technology! A-Levels test takers excluded, students of math should let the technologies do the easy work so the humans can focus on the harder jobs like making sense of the graphs, and finding the meaning of the otherwise abstract and arguably trivial math. With the help of a TI-84 emulator, Dr T plots out a fifth degree polynomial, finds its roots both algebraically and graphically, and then associates key features of the graph, its first and second derivatives.