Polynomial

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, x2 − x/4 + 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 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

Other articles related to "polynomial, polynomials":

Extensions of The Concept of A Polynomial
... Polynomials can involve more than one variable, in which they are called multivariate ... Rings of polynomials in a finite number of variables are of fundamental importance in algebraic geometry which studies the simultaneous zero sets of several such multivariate ... be constructed by repeating the construction of univariate polynomials with as coefficient ring another ring of polynomials thus the ring R of polynomials in X and Y can be viewed as the ...
Bessel Polynomials - Properties - Definition in Terms of Bessel Functions
... The Bessel polynomial may also be defined using Bessel functions from which the polynomial draws its name where Kn(x) is a modified Bessel function of the second kind ...
Schwartz–Zippel Lemma
... the Schwartz–Zippel lemma is a tool commonly used in probabilistic polynomial identity testing, i.e ... in the problem of determining whether a given multivariate polynomial is the 0-polynomial (or identically equal to 0) ... The input to the problem is an n-variable polynomial over a field F ...
Multiplicity (mathematics) - Multiplicity of A Root of A Polynomial
... Let F be a field and p(x) be a polynomial in one variable and coefficients in F ... a root of multiplicity k of p(x) if there is a polynomial s(x) such that s(a) ≠ 0 and p(x) = (x − a)ks(x) ... For instance, the polynomial p(x) = x3 + 2x2 − 7x + 4 has 1 and −4 as roots, and can be written as p(x) = (x + 4)(x − 1)2 ...
Minimax Approximation Algorithm - Polynomial Approximations
... a closed interval can be uniformly approximated as closely as desired by a polynomial function ... Polynomial expansions such as the Taylor series expansion are often convenient for theoretical work but less useful for practical applications ... to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation ...