ABSTRACT
Polynomials appear ubiquitously in linear algebra and throughout mathematics. Most of us encounter the idea of a polynomial function in calculus. In algebraic settings, one needs a more formal concept of polynomial as a symbolic expression of the form
∑n i=0 aix
i that is not necessarily a “function of x.” We begin this chapter with an intuitive description of these formal polynomials, which form a ring under the familiar algebraic rules for adding and multiplying polynomials. Then we make this intuitive discussion more precise by giving a rigorous definition of polynomials in terms of formal power series and connecting this definition with the idea of a polynomial function.
