Polynomial: Difference between revisions

Revision as of 21:32, 23 November 2002

Revision as of 21:31, 27 November 2002

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==Calculus==

In [[algebra]] and [[calculus]], a '''polynomial function''', or '''polynomial''' for short, is a [[mathematical Function|function]] of the form

'''polynomial''' for short, is a [[mathematical Function|function]] of the form

:''f''(''x'') = ''a_n xⁿ + a_n-1 x^n-1 + ... + a₁ x + a₀''

where ''x'' is a [[scalar]]-valued [[variable]], and ''a''_n are fixed scalars, called the ''[[Coefficient|coefficients]]'' of the polynomial ''f'' and the coefficient ''a_n'' is not zero. In [[calculus]], the scalars are almost always [[real number|real]] or [[complex number|complex]] numbers. More generally, they may be members of a [[Ring (algebra)|ring]].

where ''x'' is a [[variable]] ranging over the [[real number|real]] (or

[[complex number|complex]]) numbers and the ''a''₀, ... , ''a''_n are fixed

real (or complex) numbers called the ''[[Coefficient|coefficients]] of f''.

The highest occurring power (''n'') of ''x'' is called the ''degree of f''; its

coefficient ''a''_''n'' is called the ''leading coefficient''. ''a''₀ is called the ''constant coefficient'' of