does f(x)=(x-5)(x+3)(x-2) have roots of -3,5, and 2?

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.

Explore how to find the roots of the polynomial f(x) = (x-5)(x+3)(x-2) by applying the Zero Product Property. Learn why x = -3, x = 5, and x = 2 are roots, and understand the connection to polynomial factors. Suitable for high school students.

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