---
type: "concept"
title: "Multiplicity of a root"
slug: "multiplicity-of-a-root"
language: "en"
translationGroupId: "cms2z0ait0003rp01qc0mhq24"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

Let $P$ be a polynomial and $r$ a [[Root of a polynomial|root]] of $P$. The multiplicity of $P$ is the largest positive integer $k$ such that $(X-r)^{k}$ divides $P$.

##### Remarks
- A root of multiplicity 1 is also called a [[Simple root|simple root]].