Use the factor theorem to factorize `x ^(3) + x ^(2) - 4x -4` completely.

Answer

To factorize the polynomial \( f(x) = x^3 + x^2 - 4x - 4 \) using the factor theorem, we will follow these steps:

### Step 1: Identify possible rational roots
The possible rational roots of the polynomial can be found using the factors of the constant term (-4) and the leading coefficient (1). The factors of -4 are ±1, ±2, and ±4.