Definition:Polynomial Function/Real

Definition
Let $a_0, \ldots a_n \in \R$.

Then for all $x \in \R$, the expression:
 * $\forall x \in \R: \displaystyle P \left({x}\right) = \sum_{j \mathop = 0}^n \left({a_j x^j}\right) = a_0 + a_1 x + a_2 x^2 + \cdots + a_{n-1} x^{n-1} + a_n x^n$

defines a real function from $\R$ to $\R$.

This is known as a (real) polynomial function.

Coefficients
The parameters $a_0, \ldots a_n \in \R$ are known as the coefficients of the polynomial $P$.

Also see

 * Real Polynomial Function is a Real Function