Welcome guest
You're not logged in.
291 users online, thereof 0 logged in

## Definition: Polynomials

Let $$a_0,a_1,\ldots,a_n$$ be real numbers with $$a_n\neq 0$$. A real polynomial (or just a polynomial) is a function

$p:=\begin{cases} \mathbb R&\to\mathbb R\\ x&\to p(x):=a_nx^n + \ldots + a_1x + a_0\\ \end{cases}$

The numbers $$a_0,a_1,\ldots,a_n$$ are called the coefficients of the polynomial. The highest number $$n$$, for which the coefficient $$a_n\neq 0$$, is called the degree of the polynomial.

In the following interactive figure, you can drag the sliders to manipulate the values of the coefficients $$a_0,a_1,\ldots,a_5$$ and see the behavior of resulting polynomials of the degree up to $$5$$. The initial polynomial (when the Reset button is pressed) is of degree $$0$$.

| | | | | created: 2014-02-20 23:40:59 | modified: 2018-05-17 23:35:57 | by: bookofproofs