The PolynomF package is designed in such a way that it will do almost anything we might want to do with a polynomial. We highlight this package by demonstrating basic polynomial operations, calculus with polynomials, and working with a list of polynomials. Using the tools of the PolynomF package we explore the roots of degree-three polynomials, create Pascal’s triangle and a Taylor polynomial, and test two Legendre polynomial identities. Note that we open the PolynomF in the first example; it is needed for all examples in this chapter.