In mathematics, a **polynomial** is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. However, the division by a constant is allowed, because the multiplicative inverse of a non zero constant is also a constant. For example, *x*2 − *x*/4 + 7 is a polynomial, but *x*2 − 4/*x* + 7*x*3/2 is not, because its second term involves division by the variable *x* (4/x), and also because its third term contains an exponent that is not a non-negative integer (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 in computational complexity theory.

Polynomial comes from the Greek *poly*, "many" and medieval Latin *binomium*, "binomial". The word was introduced in Latin by Franciscus Vieta.

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 in calculus 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.

Read more about Polynomial: Overview, Elementary Properties of Polynomials, History, Solving Polynomial Equations, Graphs, Polynomials and Calculus, Abstract Algebra, Polynomials Associated To Other Objects, Extensions of The Concept of A Polynomial