Given the function g(n)=(n-2)(n+5)(n-3):

the coordinates of its g-intercept are 

the coordinates of its n-intercepts are 

Let's analyze the given function \( g(n) = (n - 2)(n + 5)(n - 3) \) to find its intercepts.

### 1. **g-intercept (y-intercept)**:
The g-intercept occurs when \( n = 0 \). So, substitute \( n = 0 \) into the function:

\[
g(0) = (0 - 2)(0 + 5)(0 - 3) = (-2)(5)(-3) = 30
\]

Thus, the coordinates of the g-intercept are:

\[
(0, 30)
\]

### 2. **n-intercepts (x-intercepts)**:
The n-intercepts occur where \( g(n) = 0 \). Set the function equal to 0:

\[
(n - 2)(n + 5)(n - 3) = 0
\]

This equation is satisfied when any of the factors equals zero:

- \( n - 2 = 0 \Rightarrow n = 2 \)
- \( n + 5 = 0 \Rightarrow n = -5 \)
- \( n - 3 = 0 \Rightarrow n = 3 \)

Thus, the coordinates of the n-intercepts are:

\[
(2, 0), (-5, 0), (3, 0)
\]

### Summary:
- **g-intercept**: \( (0, 30) \)
- **n-intercepts**: \( (2, 0), (-5, 0), (3, 0) \)

Do you have any questions or want further details?

Here are some related questions to consider:
1. How do you find the vertex of a quadratic or cubic function?
2. What does the sign of the leading coefficient tell you about the graph of the function?
3. How can you use the factored form of a polynomial to sketch its graph?
4. What is the significance of multiple roots in a polynomial function?
5. How does the degree of a polynomial function affect its general shape?

**Tip:** When finding intercepts, always plug \( n = 0 \) for the g-intercept and set the function equal to zero for the n-intercepts.

Given the function g(n) = (n - 2)(n + 5)(n - 3):

- the coordinates of its g-intercept are
- the coordinates of its n-intercepts are

Learn how to find the g-intercept and n-intercepts of the polynomial function g(n) = (n - 2)(n + 5)(n - 3). This problem covers factoring, intercepts, and the zero product property. Suitable for students in Grades 9-11.

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