CoefficientList

CoefficientList[poly, var]
gives a list of coefficients of powers of var in poly, starting with power 0.

CoefficientList[poly, {var₁, var₂, ...}]
gives an array of coefficients of the var_i.

The dimensions of the array returned by CoefficientList are determined by the values of the Exponent[poly, var_i].

Terms that do not contain positive integer powers of a particular variable are included in the first element of the list for that variable.

CoefficientList always returns a full rectangular array. Combinations of powers that do not appear in poly give zeros in the array.

Find the coefficients in a polynomial:

CoefficientList works even when the polynomial has not been expanded out:

Matrix of coefficients for a quadratic form: