The graph in the image represents a polynomial function, and you are asked to identify the zeros and their multiplicities.

Zeros of the Polynomial

• Zero at $x = -4$: The graph crosses the x-axis at $x = -4$, and it appears to pass straight through without flattening out, which suggests this zero has multiplicity 1.
• Zero at $x = 2$: The graph touches the x-axis at $x = 2$ and "bounces" off the axis rather than passing through it, indicating that this zero has multiplicity 2.

Common Errors

It seems like you input $x = -4$ twice with the same multiplicity of 1, which led to a mistake in the second entry. You should only list $x = -4$ once and indicate its correct multiplicity, which is 1.

Final Answer:

• $x = -4$ with multiplicity 1.
• $x = 2$ with multiplicity 2.

Would you like a further breakdown of how multiplicity affects the graph of a polynomial, or any other clarification?

Here are some related questions you might find useful:

1. How can you determine if a zero has even or odd multiplicity based on the graph?
2. What does a zero with multiplicity greater than 1 imply about the graph's behavior?
3. How can you factor a polynomial using its zeros and their multiplicities?
4. What is the general form of a polynomial given its zeros and multiplicities?
5. How does the degree of a polynomial relate to the total number of zeros (counting multiplicity)?

Tip: A zero with odd multiplicity will cause the graph to cross the x-axis, while even multiplicity results in the graph bouncing off or just touching the axis without crossing it.