# What is a Polynomial?

Nov 12, 2014

Polynomial Function of Degree n

A polynomial function $f \left(x\right)$ of degree $n$ is of the form

$f \left(x\right) = {a}_{n} {x}^{n} + {a}_{n - 1} {x}^{n - 1} + \cdots + {a}_{1} x + {a}_{0}$,

where ${a}_{n}$ is a nonzero constant, and ${a}_{n - 1} , {a}_{n - 2} , \ldots , {a}_{0}$ are any constants.

Examples

$f \left(x\right) = {x}^{2} + 3 x - 1$ is a polynomial of degree 2, which is also called a quadratic function.

$g \left(x\right) = 2 + x - {x}^{3}$ is a polynomial of degree 3, which is also called a cubic function.

$h \left(x\right) = {x}^{7} - 5 {x}^{4} + {x}^{2} + 4$ is a polynomial of degree 7.

I hope that this was helpful.