polynomial

Also known as polynomial expression

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate x is x^2 - 4x + 7. An example with three indeterminates is x^3 + 2xyz^2 - yz + 1.

AI overview

A polynomial is a mathematical expression made up of variables and numbers combined using only addition, subtraction, multiplication, and powers (with whole number exponents), with a limited number of terms—for example, x² - 4x + 7. Polynomials are fundamental building blocks in mathematics that appear throughout algebra, calculus, and countless practical applications in science and engineering.

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Commons gallery: Polynomial
Commons category: Polynomials
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~38 min read

Article

36 sections

Contents

Etymology
Notation and terminology
Definition
Classification
Operations
Addition and subtraction
Multiplication
Composition
Division
Factoring
Calculus
Polynomial functions
Graphs
Equations
Solving equations <span class="anchor" id="Solving polynomial equations"></span>
Polynomial expressions
Trigonometric polynomials
Matrix polynomials
Exponential polynomials
Related concepts
Rational functions
Laurent polynomials
Power series
Polynomial ring
Divisibility
Applications
Positional notation
Interpolation and approximation
Other applications
History
History of the notation
See also
Footnotes
Notes
References
External links

Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary 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 rings and algebraic varieties, which are central concepts in algebra and algebraic geometry.