Based on the graph shown in the image, here's how to determine the answers:

Degree of the Polynomial:

• The degree of the polynomial is related to the number of turning points. A polynomial of degree $n$ can have at most $n-1$ turning points.
• In this graph, there are 3 turning points (maximums or minimums), which means the polynomial must have a degree of at least 4.

Answer: The degree of the polynomial is at least 4.

Sign of the Leading Coefficient:

• To determine the sign of the leading coefficient, observe the end behavior of the graph:
  • For a polynomial with an even degree:
    • If the leading coefficient is positive, both ends of the graph rise as $x \to \pm \infty$.
    • If the leading coefficient is negative, both ends of the graph fall as $x \to \pm \infty$.
  • In the given graph, as $x \to \infty$, $y \to \infty$, and as $x \to -\infty$, $y \to -\infty$. This indicates the leading coefficient is positive.

Answer: The sign of the leading coefficient is positive.

Let me know if you want further clarification or have additional questions.

Here are some related questions to consider:

1. How can we verify the degree of a polynomial algebraically given its equation?
2. What are some examples of polynomial functions with positive leading coefficients?
3. How does the degree of a polynomial affect its graph's symmetry?
4. Can turning points ever indicate an odd-degree polynomial? Why or why not?
5. How does the leading coefficient test apply to odd-degree polynomials?

Tip: The degree of the polynomial always gives an upper bound to the number of turning points, so use that as your guide when analyzing graphs.