Reducible polynomials in more than one variable

Polynomials in more than one variable arise frequently in multidimensional signal processing applications. Unlike polynomials in a single variable, multidimensional polynomials cannot, in general, be factored. In this note, it is shown that the set of factorable multi-dimensional polynomials is extremely small in the sense that almost all polynomials in two or more variables are irreducible.