Numerical Analysis — properties of divided differences

Consider the following statements:

I. The $(n+1)$th divided differences of a polynomial of $n$th degree are zero, where $n$ is a natural number.

II. The $n$th divided difference for a polynomial of degree $n$ can be expressed as the quotient of two determinants each of order $n$, where $n$ is a natural number.

Which of the statements given above is/are correct?