Why is factorization useful or interesting? It is a powerful tool for simplifying polynomials, and thereby helping to comprehend them. Sometimes knowledge of the factors of a polynomial allows a large computation to be broken down into a handful of smaller calculations.

But how is it done? How does one find the factors of a polynomial? This talk presents an overview of what goes one behind the scenes when you ask the computer to factorize a polynomial. The talk will concentrate on polynomials in a single variable; factorizing multivariate polynomials is "easy" once you know how to factorize univariate polynomials.

I shall assume a little knowledge of finite fields, and some linear algebra.