##  [Factor Theorem](/factor-theorem) 

  ##  [Factor Theorem](https://algebra.quantumdictionary.io/factor-theorem-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The statement that for a polynomial p(x) over a field (or integral domain) and a scalar r, r is a root of p(x) (p(r)=0) if and only if the linear polynomial (x−r) is a factor of p(x).