Factoring in ℚ[x], II: Lagrange Interpolation

Abstract

In Chapter 8 we showed that when factoring a polynomial with integer coefficients we can always assume the factors have integer coefficients. In this chapter we use that information to describe a systematic procedure for factoring polynomials in ℤ[x]. The method is attributed to Krohecker c. 1883, but is apparently due originally to F. v. Schubert, 1793. It is based on the Chinese remainder theorem, so we begin by considering how that theorem works in K[x], K any field.