polynomial


polynomial
/pol'euh noh"mee euhl/, adj.
1. consisting of or characterized by two or more names or terms.
n.
2. Algebra.
a. (in one variable) an expression consisting of the sum of two or more terms each of which is the product of a constant and a variable raised to an integral power: ax2 + bx + c is a polynomial, where a, b, and c are constants and x is a variable.
b. a similar expression in more than one variable, as 4x2y3 - 3xy + 5x + 7.
c. Now Rare. Also called multinomial. any expression consisting of the sum of two or more terms, as 4x3 + cos x.
3. a polynomial name or term.
4. Biol. a species name containing more than two terms.
[1665-75; POLY- + (BI)NOMIAL]

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In algebra, an expression consisting of numbers and variables grouped according to certain patterns.

Specifically, polynomials are sums of monomials of the form axn, where a (the coefficient) can be any real number and n (the degree) must be a whole number. A polynomial's degree is that of its monomial of highest degree. Like whole numbers, polynomials may be prime or factorable into products of primes. They may contain any number of variables, provided that the power of each variable is a nonnegative integer. They are the basis of algebraic equation solving. Setting a polynomial equal to zero results in a polynomial equation; equating it to a variable results in a polynomial function, a particularly useful tool in modeling physical situations. Polynomial equations and functions can be analyzed completely by methods of algebra and calculus. See also orthoganal polynomial.

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Universalium. 2010.

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  • Polynomial — Pol y*no mi*al, a. 1. Containing many names or terms; multinominal; as, the polynomial theorem. [1913 Webster] 2. Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature. [1913 …   The Collaborative International Dictionary of English

  • polynomial — ● polynomial, polynomiale, polynomiaux adjectif Fonction polynomiale associée à un polynôme à une indéterminée, fonction, notée , qui à f = a0 + a1X + … + anXn associe . [ est appelé valeur du polynôme f en …   Encyclopédie Universelle

  • Polynomial — Pol y*no mi*al, n. [Poly + nomial, as in monomial, binomial: cf. F. polyn[^o]me.] (Alg.) An expression composed of two or more terms, connected by the signs plus or minus; as, a^{2} 2ab + b^{2}. [1913 Webster] …   The Collaborative International Dictionary of English

  • polynomial — 1670s (n.), 1704 (adj.), irregularly formed from POLY (Cf. poly ) + stem of BINOMIAL (Cf. binomial) …   Etymology dictionary

  • polynomial — [päl΄i nō′mē əl] n. [ POLY + (BI)NOMIAL] an expression or name consisting of more than two terms; specif., a) Algebra a linear combination of products of integral powers of a given set of variables, with constant coefficients (Ex.: x3 + 3x + 2 or …   English World dictionary

  • Polynomial — In mathematics, a polynomial (from Greek poly, many and medieval Latin binomium, binomial [1] [2] [3], the word has been introduced, in Latin, by Franciscus Vieta[4]) is an expression of finite length constructed from variables (also known as… …   Wikipedia

  • polynomial — UK [ˌpɒlɪˈnəʊmɪəl] / US [ˌpɑlɪˈnoʊmɪəl] noun [countable] Word forms polynomial : singular polynomial plural polynomials maths an expression in algebra (= a type of mathematics) that contains two or more terms Derived word: polynomial UK / US… …   English dictionary

  • polynomial — I. noun Etymology: poly + nomial (as in binomial) Date: 1674 a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (as a + bx +… …   New Collegiate Dictionary

  • Polynomial — Polynôme Courbe polynomiale cubique Un polynôme, en mathématiques, est la combinaison linéaire des produits de puissances d une ou de plusieurs indéterminées, habituellement notées X, Y, Z… Ces objets sont largement utilisés en pratique, ne… …   Wikipédia en Français

  • polynomial — 1. adjective a) Able to be described or limited by a polynomial. b) of a polynomial name or entity 2. noun a) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more… …   Wiktionary