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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

\mathbb R&\to\mathbb R\\
x&\to p(x):=a_nx^n + \ldots + a_1x + a_0\\

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

1.Proposition: Limits of Polynomials at Infinity

2.Proposition: Eveness (Oddness) of Polynomials

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)