Polynomial/Field/1/Definition

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

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

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