Concept:Use the identity x4−1=(x−1)(x+1)(x2+1) to compare factors on both sides.Explanation:Start with the given equation: (x+1)(x+p)(x2+p2)=x4−1.Factor x4−1 as (x−1)(x+1)(x2+1).Cancel the common factor (x+1) from both sides.This gives (x+p)(x2+p2)=(x−1)(x2+1).Compare the linear factors: (x+p) must equal (x−1), so p=−1.Then check: p2=1, so x2+p2=x2+1 matches the other factor.Thus the equality holds for all x.Answer:p=−1 (Option A).