examday

/TMUA

The function $f$ is defined by $f(x)=x^3+ax^2+bx+c$.

$a$, $b$ 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 $R-S$?