Answer
$(r+3s)(r+4s)$
Work Step by Step
To factor the polynomial $x^{2}+bx+c$ to $(x+p)$ and $(x+q)$, we need to have $p+q=b$ and $pq=c$.
Similarly, to factor $r^{2}+7rs+12s^{2}$ to $(r+p)$ and $(r+q)$, we need to have $p+q=7s$ and $pq=12s^{2}$
$\implies p=3s$ and $q=4s$.
Then, $r^{2}+7rs+12s^{2}=(r+3s)(r+4s)$