Problem of factoring a polynomial into lower degree polynomial

Abstract

The problem of factoring a polynomial into lower degree polynomials has a long and renowned history. D. Knuth traces back to Isaac Newton (Arithmetica Universalis, 1707) who first attempted to give a method to find linear and quadratic factors of a polynomial in Z[x]. Since then several mathematicians attempted to find irreducibility criteria for different kinds of polynomials. In modern times polynomial factorization has become a fundamental part of computer algebra systems.