To analyze this question and solve it step by step:

1. Analyze the graph:

   • The polynomial graph $y = p(x)$ crosses the x-axis at $x = -2$ and $x = 3$. These are real roots of the polynomial.
   • At $x = -2$, the graph bounces off the x-axis, indicating a double root. At $x = 3$, the graph crosses the x-axis, indicating a single root.
   • The polynomial's degree is determined by the number and types of roots. A double root at $x = -2$ and a single root at $x = 3$ give a minimum degree of 3.

2. Analyze the options:

   • (A) $(x - 3)(x + 2)$: This has roots at $x = -2$ and $x = 3$, but both are single roots. This doesn't match the graph because $x = -2$ is a double root.
   • (B) $(x + 3)(x - 2)$: This has roots at $x = -3$ and $x = 2$, which doesn't match the graph's roots.
   • (C) $(x - 3)(x + 2)^2$: This has a single root at $x = 3$ and a double root at $x = -2$. This matches the graph perfectly.
   • (D) $(x + 3)^2(x - 2)^2$: This has a double root at $x = -3$ and $x = 2$, which doesn't match the graph.

3. Conclusion:
   The correct answer is (C) $(x - 3)(x + 2)^2$.

Would you like further clarification? Here are some related questions to deepen understanding:

1. How can you determine the degree of a polynomial from its graph?
2. What is the difference between a single and a double root?
3. How do the multiplicities of roots affect the shape of a graph?
4. What happens if a root has a multiplicity of 3 or higher?
5. How can you reconstruct a polynomial from its graph?

Tip: To quickly identify root multiplicities, look for how the graph interacts with the x-axis—crossing indicates odd multiplicity, while bouncing indicates even multiplicity.