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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.
Before giving you the definition of a polynomial, it is important to provide the definition of a monomial. Definition of a monomial: A monomial is a variable, a real number, or a multiplication of one or more variables and a real number with whole-number exponents. Examples of monomials and non-monomials. Polynomial definition: A polynomial is a monomial or the sum or difference of monomials.