---
tag: 03FKX7Z5DC
kind: concept
name: Irreducible polynomial
msc: ["12E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Irreducible_polynomial
    locator: lead section
same_as:
  wikidata: Q1476663
  wikipedia: Irreducible polynomial
---

## Summary

An irreducible polynomial is a nonconstant polynomial that is not a product of two polynomials of smaller degree, over a field.
More generally, it is an irreducible element of a polynomial ring.
The [[definition of an irreducible polynomial|00X2A9G9W3]] gives the conditions.