Question: Manipulating Polynomials

If I have a polynomial in terms of x, is it possible to extract the coefficient of x^2 easily (without copying and pasting)?

The coefficients of the polynomial are large and ugly and not worth typing out.

If there's no command for getting the coefficient, perhaps I could map my polynomial (which is, say, P=ax^3 + bx^2 + cx+d) to a vector space where x^3 = (1, 0, 0) = v1, x^2 = (0, 1, 0 ) = v2, x = (0,0,1) = v3 and P = av1 + bv2 + cv3 + d.  And then the coefficient of b would be the dot product of P with v2.  But I don't know how to do this either!

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