Unit 3

There are really only 2 main ideas in Unit 3:
(1) Finding ALL roots (solutions) of any polynomial, no matter how many. We've started this (see below).
(2) Graphing polynomial functions, and describing the graphs in certain mathematical ways. We'll get to this.

For finding the roots, you must be able to:

[1] Use the Rational Root Theorem to list all the POSSIBLE roots that are either whole numbers or simple fractions (so, without square roots or i's).

[2] Use the graphing calculator ([y=], [graph], and [2nd][graph] for the table) to figure out which of the POSSIBLE whole number roots actually ARE roots.

[3] Use Synthetic Division (from Unit 2) to divide the original long polynomial by the roots you know, to reduce it down to a quadratic.

[4] Solve the quadratic that's left, using factoring or the Quadratic Formula (we learned how to do this in Unit 1).

[*] Putting all those steps together, we can take a polynomial with 3, 4, or even more roots, and get ALL of the roots.

[*] Here are some additional examples of synthetic division, that we did in support Monday/Tuesday.