PolynomialQ[expr, var] yields True if expr is a polynomial in var, and yields False otherwise.
PolynomialQ[expr, , ... ] tests whether expr is a polynomial in the .
The need not be symbols; PolynomialQ[f[a] + f[a]^2, f[a]] .
See The Mathematica Book: Section 2.3.5 and Section 3.3.2.
See also: Collect, Series.