Editing Polynomial (section)

{{Short description|Type of mathematical expression}}
{{about|the expressions themselves|the related topic in algebra|Polynomial ring}}
In [[mathematics]], a '''polynomial''' is a [[Expression (mathematics)|mathematical expression]] consisting of [[indeterminate (variable)|indeterminates]] (also called [[variable (mathematics)|variables]]) and [[coefficient]]s, that involves only the operations of [[addition]], [[subtraction]], [[multiplication]] and [[exponentiation]] to [[nonnegative integer]] powers, and has a finite number of terms.<ref>{{harvtxt|Beauregard|Fraleigh|1973|p=153}}</ref><ref>{{harvtxt|Burden|Faires|1993|p=96}}</ref><ref>{{harvtxt|Fraleigh|1976|p=245}}</ref><ref>{{harvtxt|McCoy|1968|p=190}}</ref><ref>{{harvtxt|Moise|1967|p=82}}</ref> An example of a polynomial of a single indeterminate {{math|''x''}} is {{math|''x''<sup>2</sup> − 4''x'' + 7}}. An example with three indeterminates is {{math|''x''<sup>3</sup> + 2''xyz''<sup>2</sup> − ''yz'' + 1}}.

Polynomials appear in many areas of mathematics and science. For example, they are used to form [[polynomial equation]]s, which encode a wide range of problems, from elementary [[word problem (mathematics education)|word problems]] to complicated scientific problems; they are used to define '''polynomial functions''', which appear in settings ranging from basic [[chemistry]] and [[physics]] to [[economics]] and [[social science]]; and they are used in [[calculus]] and [[numerical analysis]] to approximate other functions. In advanced mathematics, polynomials are used to construct [[polynomial ring]]s and [[algebraic variety|algebraic varieties]], which are central concepts in [[algebra]] and [[algebraic geometry]].