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For the sake of simplicity, in the sequel a (Laurent) polynomial of negative degree is understood to be the zero polynomial and, similarly, a banded matrix with negative bandwidth reduces to the zero matrix.
Degree of Polynomial. The degree is the value of the greatest exponent of any expression (except the constant) in the polynomial. To find the degree all that you have to do is find the largest exponent in the polynomial. Note: Ignore coefficients -- coefficients have nothing to do with the degree of a polynomial.