Van der Waerden obliquely acknowledges, by entitling a section 'Factorization in a Finite Number of Steps' (which applies only to factorization over the rationals), that the usual methods for factoring polynomials are not constructive. The talk will describe an algorithm for factoring polynomials with coefficients in an algebraic number field. It is contained, more or less, in an 1881 treatise of Kronecker, but Kronecker's description is very difficult to follow.