https://file.aiquickdraw.com/mathbot/file/17294385751371kjf0h1h.jpg

Let's analyze the graph and the corresponding statements about the degree 4 polynomial function.

1. **Statement A: The leading coefficient is positive.**
   - The end behavior of the graph shows that as \( x \to -\infty \), \( y \to \infty \), and as \( x \to \infty \), \( y \to \infty \). This indicates that the leading coefficient is positive for a degree 4 polynomial.
   - **This statement is true.**

2. **Statement B: The constant term is negative.**
   - The constant term is the \( y \)-intercept of the polynomial, which occurs when \( x = 0 \). From the graph, the \( y \)-intercept is positive (above the x-axis).
   - **This statement is false.**

3. **Statement C: It has 2 relative maximums.**
   - Looking at the graph, there are two points where the function has relative maximums: one near \( x = -6 \) and another around \( x = 3 \).
   - **This statement is true.**

4. **Statement D: It has 4 linear factors.**
   - A degree 4 polynomial typically has four factors if all the roots are real. This graph crosses the x-axis four times, suggesting four real roots.
   - **This statement is true.**

5. **Statement E: One of the factors is \( (x - 1) \).**
   - Looking at the x-intercepts, the function crosses the x-axis at around \( x = 1 \), so \( (x - 1) \) could be one of the factors.
   - **This statement is true.**

6. **Statement F: One of the zeros is \( x = 2 \).**
   - From the graph, it does not seem that the function crosses the x-axis at \( x = 2 \); it crosses at \( x = 1 \) and around \( x = 4 \).
   - **This statement is false.**

7. **Statement G: There is a relative minimum between \( x = 1 \) and \( x = 3 \).**
   - Indeed, there is a relative minimum around \( x = 2 \).
   - **This statement is true.**

### Correct Statements: 
- A, C, D, E, G

Would you like any further clarifications or details on these? Here are 5 related questions for deeper understanding:

1. What does the behavior of a degree 4 polynomial tell us about its graph?
2. How can we determine the number of real roots from a polynomial graph?
3. What is the significance of the leading coefficient in determining end behavior?
4. How do relative maximum and minimum points help us analyze a graph?
5. Why does the constant term correspond to the \( y \)-intercept?

**Tip:** Always check the end behavior of a polynomial by looking at the degree and sign of the leading coefficient—it gives important clues about the function's general shape.

Here is the graph of a polynomial function with degree 4. Select all of the statements that are true about the function.

Analyze the graph of a polynomial function with degree 4 to determine true statements about its behavior, relative maximums, zeros, and factors. Key concepts include polynomial end behavior, relative extrema, and the number of real roots.

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