##  [Rational Root Theorem](/rational-root-theorem) 

  ##  [Rational Root Theorem](https://algebra.quantumdictionary.io/rational-root-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

For a polynomial with integer coefficients a_n x^n + ... + a_0 where a_n and a_0 are nonzero, any rational root expressed in lowest terms p/q (q>0, gcd(p,q)=1) must have p dividing a_0 and q dividing a_n.