When P(x) is divided by x-1 the remainder is 1, and when divided by (x-2)(x-3), the remainder is 5. Find the remainder when P(x) is divided by (x-1)(x-2)(x-3).

I'm using the formula where

P(x)=(x-1)(x-2)(x-3)Q(x)+ax^2+bx+c

--

hints / steps to solve this will be greatly appreciated. thanks in advance.