Answer
$(m^2+5m+4)$ square units
Work Step by Step
The volume, $V$, of a rectangular prism is given by the formula
$$
V=Bh
,$$
where $B$ is the area of the base and $h$ is the height of the rectangular prism.
Using the formula for the volume of a rectangle, with $V=m^3+8m^2+19m+12$ and $h=m+3$, then
$$\begin{aligned}
V&=Bh
\\
m^3+8m^2+19m+12&=B(m+3)
\\
B&=\frac{m^3+8m^2+19m+12}{m+3}
.\end{aligned}
$$
Using the long division method shown below, then
$$\begin{aligned}
B&=
(m^3+8m^2+19m+12)÷(m+3)
\\&=
m^2+5m+4+\frac{\color{red}{0}}{\color{blue}{m+3}}
\\&=
m^2+5m+4
\end{aligned}
.$$Hence, the area of the shaded base of the prism, $B$, is $(m^2+5m+4)$ square units.
