Answer
The required inequality is $\left( x+3 \right)\left( x-5 \right)\le 0$.
Work Step by Step
Consider the polynomial inequality $\left( x+3 \right)\left( x-5 \right)\le 0$
Solve for $f\left( x \right)=\text{ }0$.
$\begin{align}
& {{x}^{2}}-2x-15=0 \\
& \left( x+3 \right)\left( x-5 \right)=0 \\
\end{align}$
Thus, we have
$x=-3$ and $x=5$
Therefore, $\left( x+3 \right)\left( x-5 \right)\le 0$ means $x\ge -3$ and $x\le 5$.
Hence, the solution set of $\left( x+3 \right)\left( x-5 \right)\le 0$ is $\left[ -3,5 \right]$.
The required inequality is $\left( x+3 \right)\left( x-5 \right)\le 0$.
