Explanation

x^4-1=(x^2-1)(x^2+1)=(x-1)(x+1)(x^2+1). Comparing with (x+1)(x+p)(x^2+p^2) and cancelling (x+1): (x+p)(x^2+p^2)=(x-1)(x^2+1), so p=-1. The sign is the whole question - p=+1 would give (x+1)(x^2+1), which is wrong.