Factoring bivariate polynomials with integer coefficients via Newton polygons

It is known that the Newton polygon of a polynomial carries information on its irreducibility. In this paper we shall give another proof of the main theorem and characterize the inner points of the polygon. From that proof it will be obvious that the inner points of the Newton polygon play an important role in finding possible factorizations. We shall give a necessary and sufficient condition for the existence of the integer polynomial factorization in integer factor-polynomials.