Answer
The zeros are $2,2,-1,-1,-1$.
Work Step by Step
First put $f\left( x \right)=0$. So, ${{\left( x-2 \right)}^{2}}{{\left( x+1 \right)}^{3}}=0$
Now, factorize the above equation written as:
$\left( x-2 \right)\left( x-2 \right)\left( x+1 \right)\left( x+1 \right)\left( x+1 \right)=0$
Put each factor equal to $0$. So,
$\left( x-2 \right)=0$
Or,
$\left( x-2 \right)=0$
Or,
$\left( x+1 \right)=0$
Or,
$\left( x+1 \right)=0$
Or,
$\begin{align}
& \left( x+1 \right)=0 \\
& \Rightarrow x=2,2,-1,-1,-1
\end{align}$
So, the zeros of the provided function are $2,2,-1,-1,-1$.
Graph of the function $f\left( x \right)={{\left( x-2 \right)}^{2}}{{\left( x+1 \right)}^{3}}$ shown below:
