p is a prime

I know how to prove this but I need some help in steps.

In factoring $2^p+1$ we will always have a term (2+1) because we know that $a^n + b^n = (a+b)\cdot P$ where P is a polynomial... I know this is true but I don't know how to prove it

But if i can prove the thing above then we know that one prime which satisfies the condition is 3.

And now I also need to check if that P can somehow be a prime... But i don't know how