1.6 Polynomials

Let $X$ be an indeterminate (variable) and let $a_{j}\in{\mathbb{R}}$ be coefficients for $n\in\{0,1,2,\dots\}$ and $j\in\{0,1,2,\dots\}$. A nonzero real polynomial $f(X)$ is an expression such as

We can assume that $a_{n}\neq 0$, so that the leading term $a_{n}X^{n}$ appears, and then $n$ is called the degree. We also call $a_{0}$ the constant term. The zero polynomial has undefined degree.