A real polynomial is a polynomial with real coefficients. Division of a polynomial by a number, however, yields another polynomial. The names for the degrees may be applied to the polynomial or to its terms. Mathematics of Approximation. Formation of the polynomial ring, together with forming factor rings by factoring out ideals , are important tools for constructing new rings out of known ones. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots, as, with the above definitions, every number is a root of the zero polynomial, with an undefined multiplicity. The quotient can be computed using the polynomial long division. In particular, a polynomial, restricted to have real coefficients, defines a function from the complex numbers to the complex numbers.

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