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 \(0\).