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In mathematics, a polynomial (from Greek polloi, “many” + Greek nomus, “part, portion”) 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 + 7×3/2 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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|1 Overview |
|1.1 Alternative forms |
|1.2 Polynomial functions |
|1.3 Polynomial equations |
|2 Elementary properties of polynomials |