(x - 2) and (x + 2) are the factors of x 3 + x 2 - 4x - 4. The third factor of the given polynomial is :

Given,

(x - 2) and (x + 2) are the factors of x³ + x² - 4x - 4.

⇒ (x - 2)(x + 2) = x² - 4

Thus, x² - 4 is also the factor of x³ + x² - 4x - 4.

$$\begin{array}{l} \phantom{x - 3x)}{\quad x + 1} \\ x^2 - 4\overline{\smash{\big)}\quad x^3 + x^2 - 4x - 4 } \\ \phantom{x^2 + n}\phantom(\underline{\underset{-}{+}x^3 \underset{+}{-}4x} \\ \phantom{x^2 + 3x -])7 + o)()} x^2 - 4 \\ \phantom{x^2 + 3x - ((5) + )}\underline{\underset{-}{+}x^2 \underset{+}{-}4} \\ \phantom{x^2 + 3x - 5) + 24x )}\times \end{array}$$

Thus, x³ + x² - 4x - 4 = (x² - 4)(x + 1)

= (x + 2)(x - 2)(x + 1).

Hence, option 3 is the correct option.