To determine the least possible degree of the polynomial graph shown, we analyze the behavior of the graph. Here are the steps to solve it:

1. Count the Turning Points: The graph appears to have 3 turning points (where the graph changes direction).

2. Degree and Turning Points Relationship: A polynomial of degree $n$ can have at most $n-1$ turning points. Therefore, a polynomial with 3 turning points must have a degree of at least $4$.

3. Behavior at the Ends: The graph rises on both ends, suggesting that the polynomial has an even degree.

Conclusion:

The least possible degree of the polynomial is 4.

If you'd like further details, let me know! Here are some related questions to consider:

1. How do turning points relate to the degree of a polynomial?
2. What happens to the degree of a polynomial when additional roots are added?
3. How can you distinguish between odd- and even-degree polynomials based on their graphs?
4. How does the multiplicity of roots affect the graph's shape at those roots?
5. Can you determine whether the leading coefficient is positive or negative from this graph?

Tip: To determine the degree, always start by analyzing