Polynomial - Imported Knowlpedia Content

A polynomial (in one real variable) is a function $p:\mathbb{R}\to\mathbb{R}$ of the form

p(x)=a_0+a_1x+a_2x^2+\cdots+a_n x^n

for some integer $n\ge 0$ and coefficients $a_0,\dots,a_n\in\mathbb{R}$ . If $a_n\ne 0$ , the integer $n$ is the degree of $p$ .

Remarks

Polynomials are basic examples of smooth functions (they have derivatives of all orders) and they define continuous functions on any interval, so they sit inside the space of continuous functions on that interval. Collections of polynomials often form a subalgebra of continuous functions.

Examples

$p(x)=x^3-2x+5$ is a polynomial of degree $3$ .
$p(x)=7$ is a constant polynomial (degree $0$ ), and $p(x)=0$ is the zero polynomial.