In this paper we discuss two canonical transformations that turn St��ckel separable Hamiltonians of Benenti type into polynomial form: transformation to Vi��te coordinates and transformation to Newton coordinates. Transformation to Newton coordinates has been applied to these systems only very recently and in this paper we present a new proof that this transformation indeed leads to polynomial form of St��ckel Hamiltonians of Benenti type. Moreover we present all geometric ingredients of these Hamiltonians in both Vi��te and Newton coordinates.