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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.
A constant function k of x equals 9, this is still a polynomial because we think of it as 9 times x to the 0, so the leading coefficient would be 9 and if you think of this as 9 times x to the 0 the degree is 0 this is a 0 degree polynomial. All constant functions are 0 degree polynomials.