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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.
The graph of the zero polynomial, f(x) = 0, is the X-axis. In the case of polynomials in more than one indeterminate, a polynomial is called homogeneous of degree n if all its non-zero terms have degree n. The zero polynomial is homogeneous, and, as homogeneous polynomial, its degree is undefined.