Suppose $f$ is a real valued function with domain a subset of
real numbers, $D$.

Definition: $f$ is a **polynomial function**
if **there a numbers $a_0$, $a_1$, ... , and $a_n$ so
that for any $x \in D$, $f(x) = a_nx^n + ... a_2x^2 + a_1x
+a_0 $. If**** $a_n \ne 0$ we say that $f$ is a polynomial of
degree $n$.**

**Comment: **The letters ** $a_0$, $a_1$, ..., and $a_n$**
have been used to conform with the naming of these coefficients in
quadratic functions which are polynomials of degree $2$.

The number **$a_n$ **is sometimes referred to as the
"leading coefficient " of the polynomial function.

The number **$a_1$ **is sometimes referred to as the
"linear coefficient " of the polynomial function.

The number** $a_0$** is sometimes referred to as "the $y$-
intercept," "the initial value," or the "constant " of the
polynomial function.