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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 polynomial function has the form , where are real numbers and n is a nonnegative integer. In other words, a polynomial is the sum of one or more monomials with real coefficients and nonnegative integer exponents. The degree of the polynomial function is the highest value for n where an is not equal to 0. Polynomial functions of only one term are called monomials or power functions. A power function has the form . For a polynomial function f, any number r for which is called a zero or root of the function f. When a polynomial function is completely factored, each of the factors helps identify zeros of the function.