1. The problem statement, all variables and given/known data If a , b, c are distinct and p(x) is a polynomial in x which leaves remainders a,b,c on division by (x-a),(x-b),(x-c) respectively. Then the remainder on division of p(x) by(x-a)(x-b)(x-c) is 2. Relevant equations As it is given that p(x) gives remainder a when divided by (x-a), so p(a) should be equal to a by remainder theorem.Similarl p(b) = b and p(c)=c. 3. The attempt at a solution As (x-a)(x-b)(x-c) is a cubic polynomial, remainder can be max quadratic so I assume it to be px^2 + qx + r.Again by remainder theorem we will get 3 equations for p,q,r by using a,b,c. As we see that p(a) = a, p(b)=b,p(c)=c ; Then we can say that a,b,c will be roots of px^2 +x(q-1) + r. But a quadratic polynomial can have max 2 roots. Can u please tell me what did I do wrong here?