---
type: "concept"
title: "Polynomial"
slug: "polynomial"
language: "en"
translationGroupId: "cmr4v97cr0007qu01gq9i3twj"
domain: "Algebra"
status: "usable"
aliases: []
lastEditedBy: "ancient-tree"
---

A polynomial over a [[Commutative ring|commutative ring]] $A$ is a formal expression
$$P=\sum_{i=0}^n a_i X^i=a_0+a_1 X+a_2 X^2+\cdots+a_n X^n$$
where the $a_{i}$ belong to $A$ and $a_{n}\neq 0$. $n$ is called the degree of $P$.

##### Remarks
- The set of all polynomials in $X$ with coefficients in $A$ is denoted $A[X]$.