# What is an irreducible polynomial?

##### 1 Answer

#### Answer:

An irreducible polynomial is one that cannot be factored into simpler (lower degree) polynomials using the kind of coefficients you are allowed to use, or is not factorisable at all.

#### Explanation:

**Polynomials in a single variable**

The only polynomials in a single variable that are irreducible over

**Polynomials in more than one variable**

If you are given a polynomial in two variables with all terms of the same degree, e.g.

If it is not homogeneous then it may not be possible to factor it. For example,