Answer
$6x^2-2x+5$.
Work Step by Step
The area of the rectangle is $$A= 6 x^3-20 x^2+11 x-15$$ and the length of the shortest side is $$w= x-3.$$We know that the area of a rectangle is $$A= l\times w.$$ The length of the missing side is given by: \begin{equation}
\begin{aligned}
l&= \frac{A}{w}\\
&=\frac{6 x^3-20 x^2+11 x-15}{x-3}.
\end{aligned}
\end{equation} Use synthetic division.
\begin{equation}
\begin{array}{r|rrrr}
3& 6 & -20 & 11 & -15 \\
& & 18 & -6 & 15\\
\hline & 6 & -2 & 5&0
\end{array}
\end{equation} The missing length is $6x^2-2x+5$.
