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Polynomial

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In mathematics, a polynomial (from Greek polloi, "many"[1] + Greek nomus, "part, portion"[2]) is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x (4/x) and because its third term contains an exponent that is not a whole number (3/2). The term "polynomial" can also be used as an adjective, for quantities that can be expressed as a polynomial of some parameter, as in "polynomial time" which is used incomputational complexity theory.

Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used incalculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in abstract algebra and algebraic geometry.

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| [hide]                                                                   |
|1 Overview                                                                 |
|1.1 Alternative forms                                                     |
|1.2 Polynomial functions                                                   |
|1.3 Polynomial equations                                                   |
|2 Elementary properties of polynomials                                     |
|3 History...