Factoring in ℚ[x], I

Abstract

In Chapters 3 and 4 we determined all the irreducible polynomials with real or complex coefficients, and in Chapter 7 we made a start toward finding the real roots of a general polynomial in ℝ[x]. In this chapter we begin considering the question of which polynomials with coefficients in the rational numbers ℚ are irreducible, and how to find the rational roots, or more generally the irreducible factors, of a polynomial in ℝ[x].