Degenerate polynomial forms

It is well known that the condition under which a quadratic in two variables reduces to a product of two linear factors is that the determinant of the associated quadratic form should be zero. This result is generalized to the case of a polynomial of degree n. For the degree n case there are 1/2(n - 1)n constraints for the polynomial to be reducible. A recursive algorithm is presented for determining them. Copyright (C) 1999 John Wiley & Sons, Ltd.