#### Answer

$3$

#### Work Step by Step

From the graph, the function is increasing as the value of $x$ is increasing, other than at the point $x=0$.
At $x=0$ the slope of the graph is zero, and that point is known as the point of inflection. So, the number of turning points is $2$.
$\begin{align}
& \text{Smallest}\ \text{degree}\ \text{of}\ \text{polynomial}=\left( \text{Number}\ \text{of}\ \text{turning}\ \text{point} \right)\text{+1} \\
& =2+1 \\
& =3
\end{align}$
Hence, the smallest degree of the polynomial is $3$.