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A little bit more general way: coeff[p_, x_] := Coefficient[p, x] /. (# -> 0 & /@ Variables[p]) p = x y^2 + 15 x^2 y + x + 3 y + 10; p2 = 3 t^2 + z; p3 = 3 t^2 x + z; coeff[p, x] coeff[p2, t^2] coeff[p3, t^2] coeff[p3, x t^2] (* 1 3 0 3 *)


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I'm going to restrict to the case of rational coefficients. There are ways to extend to complex rational coefficients but that's more than I have time or desire to consider right now. I'll illustrate an efficient methodology with this example. Along the way I will say a bit about modest improvements that can be made. We'll start with the polynomial and the ...



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