Based on the provided graph of a degree 5 polynomial, we need to determine the x-values of the roots and their multiplicities.

Analyzing the graph:

1. Root at x = -4:

   • This root crosses the x-axis at $x = -4$ and the behavior suggests it has multiplicity 1. This is because the graph crosses the x-axis sharply.

2. Root at x = 2:

   • The graph touches the x-axis at $x = 2$ without crossing it, indicating this is a root with multiplicity 2.

3. Other roots:

   • The graph crosses the x-axis again near $x = 0$, which suggests a root at $x = 0$ with multiplicity 1.

Updated table:

Would you like further details or have any questions?

Here are 5 related questions:

1. What is the general shape of a degree 5 polynomial based on its behavior at infinity?
2. How does multiplicity affect the graph of a polynomial at its roots?
3. What is the difference between even and odd multiplicity in terms of graph behavior?
4. Can you identify other key features of polynomials based on their graphs?
5. How do the number of roots and their multiplicities relate to the degree of the polynomial?

Tip: Always check how the graph behaves at the x-axis to determine the root's multiplicity—crossing means odd multiplicity, touching means even.