## 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, *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.

Read more about Polynomial.

### Some articles on polynomial:

**Polynomial**

... Let F be a field and p(x) be a

**polynomial**in one variable and coefficients in F ... F is called 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 ...

**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 ... alternatively 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 ...

... In mathematics, 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 ...

**Polynomial**s - 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 and yn(x) is ...

**Polynomial**Approximations

... function defined on 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 ... desirable 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 ...

### More definitions of "polynomial":

- (
*adj*): Having the character of a polynomial.

Example:*"A polynomial expression"*

Synonyms: multinomial