The question of how to certify the non-negativity of a polynomial function lies at the heart of Real Algebra and has important applications to optimization. Building on work by Choi, Lam, and Reznick , as well as Harris , Timofte  provided a remarkable method to efficiently certify non-negativity of symmetric polynomials. In this note we slightly generalize Timofte's statements and investigate families of polynomials that allow special representations in terms of power-sum polynomials. We also recover the consequences of Timofte's original statements as a corollary. (C) 2015 Elsevier B.V. All rights reserved.