I3.3 If $R$ is a positive integer and $R^{3}+4 R^{2}+(Q-93) R+14 Q+10$ is a prime number, find the value of $R$. (Reference: $\mathbf{2 0 0 4}$ FI4.2)
Let $f(R)=R^{3}+4 R^{2}-80 R+192$
$f(4)=64+64-320+192=0 \Rightarrow x-4$ is a factor
By division, $f(R)=(R-4)\left(R^{2}+8 R-48\right)=(R-4)^{2}(R+12)$
$\because f(R)$ is a prime number
$\therefore R-4=1 \Rightarrow R=5$ and $R+12=17$, which is a prime.