HMMT 2001 T4

P is a polynomial. When P is divided by $x-1$, the remainder is -4 . When P is divided by $x-2$, the remainder is -1 . When $P$ is divided by $x-3$, the remainder is 4 . Determine the remainder when P is divided by $x^{3}-6 x^{2}+11 x-6$.