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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.
Definition of Polynomial. A polynomial is a monomial or a sum or difference of two or more monomials. Polynomial function: A polynomial function is a function whose terms each contain a constant multiplied by a power of a variable. P(x) = a0xn + a1xn-1 + .................+ an-2x2 + an-1x + an is a polynomial function. where a0, a1, a2,..., an are all real numbers and n is a non-negative integer.