Polynomials in Depth
Welcome to our In Depth course on polynomials. Our In Depth courses, take a subject from its foundations, often at the high school level, and follows it all the way through to the graduate level. In this course, we'll be giving this in depth treatment to polynomials in
- Basics (Introductory Algebra) covers definitions and ways that we classify polynomials.
- Arithmetic (Introductory Algebra) goes over methods for adding, subtracting, multiplying and dividing polynomials. You'll find the FOIL method described in this chapter.
- Factoring, Part 1 (Introductory Algebra) reviews common techniques for factoring polynomials including "factoring by grouping".
- Solving Equations (Introductory Algebra) covers methods for solving polynomial equations including the zero product rule and the quadratic forumla.
- Quadratic Polynomials (College Algebra - pending) have enough special properties and general usefulness that they rate some individual attention.
- Factoring, Part 2 (Precalculus) expands on factoring methods including Descartes' Rule of Signs and the Rational Root Theorem.
- Graphing (Precalculus - pending) covers special topics related to the graph of a polynomial including multiplicity and end behavior.
- Approximation and Curve Fitting (Calculus+ - pending) finishes our tour with advanced techniques related to numeric analysis and approximation theory including the Weirstrass Approximation Theorem, Taylor Series, Lagrange polynomials and interpolation methods.
Our Approach to Teaching and Learning
Math is a little unusual in the academic world. Unlike a lot of subjects, you're expected to actually be able to do the math by the time the class is done. You can't get there by watching other people do math or reading it about it in a book. You have to get out a pencil and paper and do it for yourself. The video lectures are a good starting point for your study but you should also spend time working on the exercises and the "explorations" material. Important concepts are discussed in the Explorations material and the associated videos as well as in the main lectures. Problems in the Practice sections marked with a star are particularly important. You should try to solve those on your own based on the lecture material but it's also worth checking out the posted solutions for additional important techniques and concepts.
This class covers a wide range of topics at a wide variety of levels. The first four chapters are what would be covered in an introductory high school or undergraduate algebra class. The next three sections come from high school 'Algebra 2' or an undergraduate College Algebra class. The modeling and approximation material uses first and second semester calculus and a few topics from graduate level analysis.
Time to Completion
While the class includes some practice material and questions, it's not really intended as a complete, step-by-step course. It's more useful as a supplement if you need more information on a specific topic or method that's being covered in another class.