Cover-up idea After clearing denominators: P(x)=A(x−2)(x−3)+B(x−1)(x−3)+C(x−1)(x−2)P(x)=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2)P(x)=A(x−2)(x−3)+B(x−1)(x−3)+C(x−1)(x−2) Substituting x=1,2,3x=1,2,3x=1,2,3 directly gives A,B,CA,B,CA,B,C.