Condition for polynomial factoring

Question

I encountered a sum , prove that $x²+px+p²$ would be a factor of $(x+p)^n–x^n–p^n$ if $n$ be odd and not a multiple of $3$. I tried breaking $(x+p)^n$ by binomial but it became more complicated and also tried factoring the dividend polynomial into $(x+p)[(x+p)^{n-1}–(x^{n-1}–......p^{n-1})]$ but to no avail . Can anyone please help by telling which way of viewing this problem am i overlooking or not thinking. Can anyone please enlighten me? I don't want a full detailed solution i can work that on my own i just want the path to do it.

Answer 1

Hint: $$(x^2+px+p^2)(x-p)=x^3-p^3$$

Now, can you do it?