On the Infinite Increase of a Class of Polynomials

(or , respectively) denotes the set of polynomials in variables with real coefficients such that as (respectively, as . The necessary and sufficient conditions for (or for , respectively) are obtained in terms of degree , the geometrical structure of the Newton polyhedron of polynomial , and the multiplicity of zeros of its main homogeneous subpolynomial . The geometrically illustrative sufficient conditions are found for for generalized homogeneous polynomials in three variables.