Polynomial function

Math Glossary

A resource for WE & Friends Mathematics and Science Projects

Home  | A  | B  | C  |  D  | E  | F  | G  | H  |  I  | J  | K  | L  | M  | N  | O  | P  | Q  | R  | S  | T  | U  | V  | W  | X  | Y  | Z

This glossary is far from complete. We are constantly adding math terms.
For instructions on adding new terms, please refer to Math Glossary Main Page

Definition

Polynomial function A polynomial function [math]P\,[/math] is one defined for all real [math]x\,[/math] by an equation on the form [math]P(x)=c_0+c_1x+\cdots+c_nx^n=\sum_{k=0}^n c_kx^k\,[/math] the numbers [math]c_0, c_1, \cdots, c_n\,[/math] are called the coefficient of the polynomial, and the nonegative integer [math]n\,[/math] is called its degree if [math]c_n\neq0\,[/math]. They include the constant functions and the power functions as special cases. Polynomials of degree 2, 3 and 4 are called quadratic, cubic, and quartic polynomials, respectively.

Examples

[math]\text{Polynomial function }\,[/math][math]P(x)=\frac{1}{2}x^4+3x^2\,[/math]

[math]x\,[/math]	[math]P(x)\,[/math]
[math]-5\,[/math]	[math]387.5\,[/math]
[math]-4\,[/math]	[math]176.0\,[/math]
[math]-3\,[/math]	[math]67.5\,[/math]
[math]-2\,[/math]	[math]20.0\,[/math]
[math]-1\,[/math]	[math]3.5\,[/math]
[math]0\,[/math]	[math]0.0\,[/math]
[math]1\,[/math]	[math]3.5\,[/math]
[math]2\,[/math]	[math]20.0\,[/math]
[math]3\,[/math]	[math]67.5\,[/math]
[math]4\,[/math]	[math]176.0\,[/math]
[math]5\,[/math]	[math]387.5\,[/math]

Web Resources

Wikipedia - Polynomial functions