ABSTRACT
The fifth chapter presents the standard topic of many mathematical courses: polynomials. It starts from considering the binomial expansion and proves several great theorems about it and about the Pascal triangle. Next, it builds up systematic ways of how to deal with polynomials: how to determine if the two polynomials are identically equal, what are the roots of a polynomial, and so on. It presents three proofs of the familiar quadratic formula, a proof of Vieta's theorem, and of the polynomial remainder theorem. The Fundamental Theorem of Algebra is introduced, but a sketch of its proof is delayed until chapter 7.
