# Polynomial/Field/1/Definition

Polynomial in one variable

Polynomial in one variable

Let ${}K$ be a field. An expression of the form

- ${}P=a_{0}+a_{1}X+a_{2}X^{2}+\cdots +a_{n}X^{n}\,,$

with
${}a_{i}\in K$
and
${}n\in \mathbb {N}$,
is called a * polynomial in one variable* over ${}K$.