To solve this problem, we need to identify the zeros of the function $f(x)$ from the graph provided, and then use those zeros to determine the factors of $f(x)$.

Steps to Solve:

1. Identify the zeros from the graph: The zeros (x-intercepts) are the points where the graph crosses the x-axis, i.e., where $f(x) = 0$.

   From the graph, it appears the function crosses the x-axis at the following points: $x = -8, \, x = 2, \, x = 6$

2. Apply the factor theorem: According to the factor theorem, if $x = a$ is a root of $f(x)$, then $(x - a)$ is a factor of $f(x)$.

   Therefore, the factors corresponding to the zeros are: $(x + 8), \, (x - 2), \, (x - 6)$

Thus, the factors of $f(x)$ are: $(x + 8), (x - 2), (x - 6)$

Would you like any more details on this solution? Here are some follow-up questions:

Follow-up Questions:

1. What is the general form of a polynomial function given its factors?
2. How can you reconstruct the polynomial $f(x)$ from the factors $(x + 8)(x - 2)(x - 6)$?
3. What happens if one of the zeros has a higher multiplicity (i.e., the graph touches the x-axis but does not cross)?
4. How can you determine if a factor is quadratic or linear from the graph alone?
5. How would the graph look if some of the zeros were non-integer values?

Tip:

To find the full polynomial function from its factors, multiply the factors together using the distributive property or a method like FOIL for binomials.