What is an irreducible polynomial?
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.
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,