TMUA 2018 Paper 1 Question 5

The function $f$ is defined by $f(x)=x^3+a{x}^2+bx+c$. $a$, $b$ and $c$ take the values $1$, $2$ and $3$ with no two of them being equal and not necessarily in this order. The remainder when $f(x)$ is divided by $(x+2)$ is $R$. The remainder when $f(x)$ is divided by $(x+3)$ is $S$. What is the largest possible value of $R-S$?