Polynomial

definitionfield-theoryvector-spaces

Definition

A polynomial is a function $p:\mathbb{F}\to \mathbb{F}$ such that $p(z)=a_0+a_{1}z+a_2{z}^2+\cdots +a_m{z}^m$, for all $Z\in \mathbb{F}$.

$P(\mathbb{F})$ is the set of all polynomials with coefficients in $\mathbb{F}$.

The degree of $p\in P(\mathbb{F})$ is $m$ if $p(z)=a_0+a_{1}z+\cdots +a_m{z}^m$ and $a_m\ne 0$.

Examples