Polynomial devision

[Gabriellaeid]

I would be glad if someone could help me prove the following is correct for every n who belong to the natural numbers

 

[R.M.]

Start multiplying. What is x times the first five terms? What is -1 times the first five terms? Notice anything about the terms?

 

[Harry_the_cat]

Alternatively you could do a proof by induction which falls out quite nicely.