You have the polynomial \( P(x) = x^3 - 2x^2 - 4x + 8 \). Would you like to analyze its properties or solve for something specific? Here are a few directions we can take:

1. **Find the roots**: Solve for \( P(x) = 0 \).
2. **Find the derivative**: To analyze the rate of change or critical points.
3. **Factor the polynomial**: If it can be factored easily.
4. **Evaluate at specific points**: Plug in values of \( x \).
5. **Graph the polynomial**: Visualize its behavior.

Let me know what you'd like to explore, or feel free to upload a photo if needed!

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Here are five related questions:

1. What are the roots of \( P(x) \)?
2. What is the derivative \( P'(x) \)?
3. Can \( P(x) \) be factored?
4. What are the critical points of \( P(x) \)?
5. What is the behavior of \( P(x) \) as \( x \to \infty \)?

**Tip**: A good place to start with polynomials is by finding their derivative for critical points and understanding their turning behavior.

Explore the properties of the cubic polynomial P(x) = x³ - 2x² - 4x + 8. Learn how to find its roots, calculate its derivative for critical points, and factor the polynomial. This is an essential topic for students in Grades 10-12 studying polynomial functions and calculus.

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