The factor common to the two polynomials x 2 - 4 and x 3 - x 2 - 4x + 4

Factorize :

⇒ x² - 4

⇒ (x - 2)(x + 2)

Factorize :

⇒ x³ - x² - 4x + 4

⇒ (x³ - x²) - (4x - 4)

⇒ x²(x - 1) - 4(x - 1)

⇒ (x - 1)(x² - 4)

⇒ (x - 1)(x² - 2²)

⇒ (x - 1)(x - 2)(x + 2).

Common factors between x² - 4 and x³ - x² - 4x + 4 = (x - 2) and (x + 2).

Hence, option 3 is the correct option.