Answer
$5$
Work Step by Step
From the graph, the curve of the function is decreasing, then increasing as the value of $x$ increases for $x<0$.
At $x=0$ the slope of the graph is zero; that point is known as the point of inflection.
The curve of the function is decreasing, then increasing as the value of $x$ increases for $x>0$.
So, the number of turning points is $4$.
$\begin{align}
& \text{Smallest}\ \text{degree}\ \text{of}\ \text{polynomial}=\left( \text{Number}\ \text{of}\ \text{turning}\ \text{point} \right)\text{+1} \\
& =4+1 \\
& =5
\end{align}$
Hence, the smallest degree of the polynomial is $5$.
