Answer
$r^{2}+11r+24=(r+3)(r+8)$
Work Step by Step
$11$ is positive, so we list positive factors of $24$.
$\left[\begin{array}{lll}
\text{Factors of 24 } & \text{Sum of factors}\\
1 \text{ and }24 & 25\\
2\text{ and } 12 & 14 & \\
3\text{ and }8 & 11 & \text{is what we need}\\
4\text{ and }6 & 10 &
\end{array}\right]$
$r^{2}+11r+24=(r+3)(r+8)$
Check:
$(r+3)(r+8)=$
...use the FOIL method.
$=r^{2}+8r+3r+24$
...add like terms.
$=r^{2}+11r+24$
