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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.
If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say that r has multiplicity k. Zeroes with a multiplicity of 1 are often called simple zeroes. For example, the polynomial will have one zero, , and its multiplicity is 2.