If $\displaystyle a(x)$ and $\displaystyle b(x)$ are coprime in $\displaystyle \mathbb{Z}_n[x]$ and $\displaystyle a(x) \mid f(x), b(x) \mid f(x)$ in $\displaystyle \mathbb{Z}_n[x]$, then is it true that $\displaystyle a(x)b(x) \mid f(x)$ in $\displaystyle \mathbb{Z}_n[x]$?