https://file.aiquickdraw.com/mathbot/file/1727504220124s0upxfib.jpg

Let's break down and solve the problems in the image:

### Part a) Finding the roots of the polynomial \( f(x) = (x - 1)(x - 3)(x + 2) \):

To find the roots of \( f(x) \), we set each factor of the polynomial equal to zero and solve for \( x \):

1. \( x - 1 = 0 \) → \( x = 1 \)
2. \( x - 3 = 0 \) → \( x = 3 \)
3. \( x + 2 = 0 \) → \( x = -2 \)

Thus, the roots of \( f(x) \) are \( x = 1, 3, -2 \).

### Part b) Solving \( 0 = x^2 - x - 2 \):

This is a quadratic equation. To solve it, we can factor the quadratic:

\[
x^2 - x - 2 = (x - 2)(x + 1)
\]

Now, set each factor equal to zero:

1. \( x - 2 = 0 \) → \( x = 2 \)
2. \( x + 1 = 0 \) → \( x = -1 \)

Thus, the solutions are \( x = 2, -1 \).

### Summary of answers:
- **Part a**: Roots of \( f(x) \): \( 1, 3, -2 \)
- **Part b**: Solutions: \( 2, -1 \)

Would you like more details on any of these steps?

Here are five related questions:
1. How do you solve higher-degree polynomials?
2. What is the quadratic formula, and when should it be used?
3. How can you verify that the roots you found are correct?
4. What are complex roots, and when do they occur in polynomials?
5. Can a quadratic equation have more than two real roots?

**Tip**: When solving quadratic equations, always check if the equation can be factored before using the quadratic formula—it saves time!

Find the roots of the polynomial f(x) = (x - 1)(x - 3)(x + 2) and solve the quadratic equation 0 = x^2 - x - 2.

Learn how to find the roots of the polynomial f(x) = (x - 1)(x - 3)(x + 2) and solve the quadratic equation 0 = x^2 - x - 2 through factoring. This tutorial covers important algebraic concepts, including factoring and the zero product property, suitable for students in Grades 7-10.

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