5.0: Introduction – Polynomials

Chapter 5: Polynomials

This chapter is two-fold. First, we will formally define what a polynomial is, and study the various representations of polynomials and how to convert between them (a challenging problem in its own right). We will also study the nature of polynomial factors and roots. Then, we will shift gears and study polynomials from a combinatorial perspective, by looking at ways to expand the product of several linear polynomials cleverly, as well as applying our knowledge of Pascal’s Triangle to study the Binomial Theorem and its applications.

There is no way that we can study all possible aspects of polynomials in just a few weeks, so we’ve curated a set of relevant topics. No calculus is necessary, but an understanding of basic calculus may help you understand these concepts beyond what we cover.