Factors of 4 + 4x - x² - x³ are :

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

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

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

4. (2 + x)(x - 1)(2 - x)

Substituting x = 2 in 4 + 4x - x² - x³, we get :

⇒ 4 + 4x - x² - x³

⇒ 4 + 4(2) - 2² - 2³

⇒ 4 + 8 - 4 - 8

⇒ 0.

∴ (x - 2) is the factor of 4 + 4x - x² - x³.

Dividing -x³ - x² + 4x + 4 by (x - 2),

$\begin{array}{l} \phantom{x - 2)}{-x^2 -3x - 2} \ x - 2\overline{\smash{\big)}-x^3 - x^2 + 4x + 4} \ \phantom{x - 2)}\phantom{2}\underline{\underset{+}{-}x^3 \underset{-}{+}2x^2} \ \phantom{{x - 2}x^3-2}-3x^2 + 4x \ \phantom{{x - 2)}x^3-2}\underline{\underset{+}{-}3x^2 \underset{-}{+} 6x} \ \phantom{{x - 2)}{x^3-2x^{2}(3)}}-2x + 4 \ \phantom{{x - 2)}{x^3-2x^{2}(31)}}\underline{\underset{+}{-}2x \underset{-}{+} 4} \ \phantom{{x - 2)}{x^3-2x^{2}(31)}{-2x}}\times \end{array}$

we get quotient = -x² - 3x - 2.

∴ -x³ - x² + 4x + 4 = (x - 2)(-x² - 3x - 2)

= (x - 2)[-x² - 2x - x - 2]

= (x - 2)[-x(x + 2) - 1(x + 2)]

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

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

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

Rearranging the terms we get,

⇒ (2 + x)(2 - x)(1 + x)

Hence, Option 1 is the correct option.