You have the polynomial expression:

$f(x) = x^3 + 2x^2 - 4x - 8$

Is there a specific operation you would like to perform with this polynomial (e.g., factorization, solving for roots, derivative, etc.)? Please clarify so I can assist you further!

Would you like me to:

1. Factor the polynomial?
2. Find the roots of the polynomial using methods like synthetic division or the Rational Root Theorem?
3. Calculate the derivative of the polynomial?
4. Evaluate the polynomial at a specific value of $x$?
5. Perform any other operation with the given polynomial?

Tip: To factor cubic polynomials, one common approach is to first find a possible rational root using the Rational Root Theorem, and then use synthetic or long division to reduce the polynomial.