TITLE: Is there any geometrical definition of polynomials?
QUESTION [7 upvotes]: We know that a polynomial in single variable/indeterminate is defined algebraically as-

An expression of the form $a_{n}x^n+a_{n-1}x^{n-1}+\dots+a_{2}x^2+a_{1}x+a_{0}$,  where $a_n,\dots,a_0$ are constants/parameters and $x$ is the indeterminate/variable.

But I was wondering if polynomial have any geometrical meaning.

REPLY [3 votes]: A curve which after certain successive differentiations gives zero at all points. You will get a straight line parallel to  x axis at the end at all points.