Sylvester matrix function

SylvesterMatrix[poly1_, poly2_, var_] := With[{coeffs1 = Reverse[CoefficientList[poly1, var]], coeffs2 = Reverse[CoefficientList[poly2, var]], l1, l2},
   l1 = Length[coeffs1]; l2 = Length[coeffs2];
   Join[If[l2 - 2 > 0, NestList[RotateRight, PadRight[coeffs1, l1 + l2 - 2], l2 - 2], {}],
        If[l1 - 2 > 0, NestList[RotateRight, PadRight[coeffs2, l1 + l2 - 2], l1 - 2], {}]]]