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    Polynomial

    Basic definition

    A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

    Detailed definition

    A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate polynomial) with constant coefficients is given by a_n x^n + ... + a_2 x^2 + a_1 x + a_0. The individual summands with the coefficients (usually) included are called monomials, whereas the products of the form x_1^(a_1) ...x_n^(a_n) in the multivariate case, i.e., with the coefficients omitted, are called terms. However, the term "monomial" is sometimes also used to mean polynomial summands without their coefficients, and in some older works, the definitions of monomial and term are reversed. Care is therefore needed in attempting to distinguish these conflicting usages.

    Related terms

    Abel polynomial | actuarial polynomial | Bell polynomial | Bernoulli polynomial | Bernoulli polynomial of the second kind | Bernstein polynomial | Bessel polynomial | Bézout's theorem | binomial | Bombieri inner product | Bombieri norm | Boole polynomial | Chebyshev polynomial of the first kind | Chebyshev polynomial of the second kind | Christoffel-Darboux formula | Christoffel number | complex number | cyclotomic polynomial | Descartes' sign rule | Durfee polynomial | Ehrhart polynomial | Euler four-square identity | Faber polynomial | Fibonacci identity | fundamental theorem of algebra | fundamental theorem of symmetric functions | Gauss-Jacobi mechanical quadrature | Gegenbauer polynomial | Gould polynomial | Gram-Schmidt orthonormalization | greatest lower bound | Hermite polynomial | Hilbert polynomial | irreducible polynomial | isobaric polynomial | isograph | Jensen polynomial | Krawtchouk polynomial | Laguerre polynomial | least upper bound | Legendre polynomial | Liouville polynomial identity | Lommel polynomial | Lukács theorem | Mahler polynomial | Meixner polynomial of the first kind | Meixner polynomial of the second kind | Mittag-Leffler polynomial | monomial | Mott polynomial | multivariate polynomial | Narumi polynomial | orthogonal polynomials | perimeter polynomial | Peters polynomial | Pidduck polynomial | Poisson-Charlier polynomial | Pollaczek polynomial | polynomial discriminant | polynomial equation | polynomial factorization | polynomial function | polynomial identity | polynomial norm | polynomial roots | power polynomial | quarter squares rule | Ramanujan 6-10-8 identity | rational function | root | Runge's theorem | Schläfli polynomial | separation theorem | Stieltjes-Wigert polynomial | Stirling polynomial | trinomial | trinomial identity | univariate polynomial | Weierstrass's polynomial theorem | Zernike polynomial

    Educational grade level

    middle school level (California Algebra I standard)

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