First, I will explain why the $\left(n+1\right)$st difference sequence is zero for sequence data generated by an $n$th degree polynomial. Then, I will use difference equations to show that if a sequence has its $(n+1)\text{st}$ difference sequence equal to zero, and $n+0$ is the smallest such integer, then a polynomial of degree $n$ can generate the sequential data. The difference equation approach is new. But, more can be said about the polynomial; I will review others' results on how to construct the polynomial.