This is what I have so far, if this is not enough to help, you may need to wait for someone more knowledgeable.
If you checked the n=1 case, then you will need to assume that the n=k case is true. From there you should be able to prove that the n=k+1 case is true. (This is normally how the induction method works)
Assume is a numerical polynomial. Then
Now use the fact that is a numerical polynomial. You should be able to concentrate on the factor .