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Categories: Abstract algebra Complex analysis Numerical analysis Polynomials Cleanup from September 2008 All pages needing cleanup |
Summary Of: PolynomialA polynomial is either zero... A polynomial is a sum of terms... When a polynomial in one variable is arranged in the traditional order... zero polynomial is the largest degree of any one term... the polynomial has degree two... An expression that can be converted to polynomial form through a sequence of applications of the... is a polynomial because it can be worked out to... is not a polynomial because it includes division by a variable... of one argument is called a polynomial function if it satisfies... is a polynomial function of one argument... Polynomial functions of multiple arguments can also be defined... Polynomial functions are an important class of... in which a polynomial is set equal to another polynomial... In case of a polynomial equation the variable is considered an... A polynomial equation is to be contrasted with a... where both members represent the same polynomial in different forms... of a polynomial function is a polynomial function... of a polynomial function is a polynomial function... also have a factored form in which the polynomial is written as a product of linear polynomials... Every polynomial in one variable is equivalent to a polynomial with the form... is sometimes taken as the definition of a polynomial in one variable... for solving all first degree and second degree polynomial equations in one variable... of polynomial equations is a set of equations in which a given variable must take on the... in the general formula for a polynomial in one variable... Every polynomial corresponds to a polynomial function... where the polynomial is set equal to zero... of the polynomial and they are the... polynomial has at least one distinct root... for the roots of a polynomial of degree 5 or greater in terms of its coefficients... Numerically solving a polynomial equation in one unknown is easily done on computer by the... that the roots of any polynomial may be expressed in terms of multivariate... A polynomial function in one real variable can be represented by a... The graph of any polynomial with degree 2 or greater... Polynomial graphs are analyzed in calculus using intercepts... Polynomial of degree 2... Polynomial of degree 2... Polynomial of degree 2... Polynomial of degree 3... Polynomial of degree 3... Polynomial of degree 3... Polynomial of degree 4... Polynomial of degree 4... Polynomial of degree 4... Polynomial of degree 5... Polynomial of degree 5... Polynomial of degree 5... furthermore any polynomial is equal to any polynomial with greater value of... Thus each polynomial is actually equal to the sum of the terms used in its formal expression... is interpreted as a polynomial that has zero coefficients at all powers of... One reason that algebraists distinguish between polynomials and polynomial functions is that over some rings different polynomials may give rise to the same polynomial... more important reason to distinguish between polynomials and polynomial functions is that many operations on polynomials... require looking at what a polynomial is composed of as an expression rather than evaluating it at some constant value for... notion of polynomial function at all... One can start by simply checking if the polynomial has linear factors... A polynomial in one variable is called a... a polynomial in more than one variable is called a... the terms of a univariate polynomial are completely ordered by their degree... zero or else the polynomial would not be of degree... a polynomial of degree 4 or higher is referred to as a... polynomial of degree n... for the degrees may be applied to the polynomial or to its terms... a constant may refer to a zero degree polynomial or to a zero degree term... Rather the degree of the zero polynomial is either left explicitly undefined... some notions such as degree or whether a polynomial is considered monic can change between these points of view... any individual polynomial can only contain finitely many variables... Shows that the roots of any polynomial may be written in terms of multivariate hypergeometric functions... Polynomial solutions in terms of theta functions...Encyclodia Page On: Polynomial |
