Coefficient[expr, form] gives the coefficient of form in the polynomial expr.
Coefficient[expr, form, n] gives the coefficient of form^n in expr.
Coefficient picks only terms that contain the particular form specified. is not considered part of .
form can be a product of powers.
Coefficient[expr, form, 0] picks out terms that are not proportional to form.
Coefficient works whether or not expr is explicitly given in expanded form.
See The Mathematica Book: Section 1.4.7 and Section 3.3.2.
See also: Exponent, SeriesCoefficient.