Yes, the function $f(x) = (x - 5)(x + 3)(x - 2)$ has roots of $-3$, $5$, and $2$.

In this function, each factor corresponds to a root:

• $x - 5 = 0$ when $x = 5$,
• $x + 3 = 0$ when $x = -3$,
• $x - 2 = 0$ when $x = 2$.

Thus, the roots of $f(x)$ are indeed $x = -3$, $x = 5$, and $x = 2$.

Would you like more details on the process or have any other questions?

Here are some related questions to deepen your understanding:

1. What happens to the graph of $f(x)$ near each root?
2. How does the sign of each factor change near each root?
3. What is the degree and leading coefficient of $f(x) = (x - 5)(x + 3)(x - 2)$?
4. How can we expand $f(x) = (x - 5)(x + 3)(x - 2)$ to find the polynomial form?
5. What does the graph of $f(x) = (x - 5)(x + 3)(x - 2)$ look like?

Tip: Each root of a polynomial corresponds to an $x$-intercept on its graph.