Question

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is ______.

Options

• (x + 1)

• (x − 1)

• (x − 2)

• (x − 4)

Answer 1

The factor common to the two polynomials x² − 4 and x³ − x² − 4x + 4 is (x − 2).

Explanation:

⇒ 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 (x − 2) is the correct option.