https://file.aiquickdraw.com/mathbot/file/1728533442108ad5zs8u0.jpg

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.

Use the graph to identify zeros and multiplicity. Based on the graph, recall that zeros of a function are values of x at which y = 0. Considering each zero, what is the multiplicity of each zero?

Learn how to identify zeros and their multiplicities using a polynomial graph. This problem involves analyzing the behavior of the graph at x = -4 and x = 2 to determine the correct multiplicities. Suitable for high school students studying polynomial functions.

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