ABSTRACT
In this appendix, we develop the elementary properties of polynomials that are used in the text.
Definition 492 Let F be a field. Then the ring of polynomials F [x] is the set of all expressions of the form
a0 + a1x+ a2x2 + . . . ,
where a0, a1, . . . ∈ F and there exists M ≥ 0 such that ak = 0 for all k ≥ M . Each such expression is called a polynomial in the indeterminate x. We say that the degree of a0 + a1x + a2x2 + . . . is undefined if all of the coefficients a0, a1, . . . are 0; otherwise, the degree is the largest integer n such that an = 0.
