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.