where cn, cn-1, …, c2, c1 and c0 are constants, the coefficients of this polynomial. Here the term cnxn is called the leading term and its coefficient cn the leading coefficient; if the leading coefficient is 1, the univariate polynomial is called monic. Note that apart from the leading coefficient cn (which must be non-zero or else the polynomial would not be of degree n) this general form allows for coefficients to be zero; when this happens the corresponding term is zero and may be removed from the sum without changing the polynomial. It is nevertheless common to refer to ci as the coeffient of xi, even when ci happens to be 0, so that xi does not really occur in any term; for instance one can speak of the constant term the polynomial, meaning c0 even if it should be zero.
Polynomials can similarly be classified by the kind of constant values allowed as coefficients. One can work with polynomials with integral, rational, real or complex coefficients, and in abstract algebra polynomials with many other types of coefficients can be defined. Like for the previous classification, this is about the coefficients one is generally working with; for instance when working with polynomials with complex coefficients one includes polynomials whose coefficients happen to all be real, even though such polynomials can also be considered to be a polynomials with real coefficients.