If p(x) is a polynomial, which when divided (x-1) gives a remainder of 2 and when divided by (x-2) gives a remainder of 1. What is the remainder when it is divided by (x-1)(x-2)?

I have been able to get answers for a few polynomials(eg. -(x^2)/3 + 7/3) that give those remainders, but how do you solve it in general?