2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111620In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester's formula was also recently proved by Lascoux and Pragacz by using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants.9 pages, no figures, simpler proof of the main results thanks to useful comments made by the referees. To appear in Journal of Symbolic ComputationCommutative AlgebraAlgebraic Geometry14Q10;68W30text