Which of the following is a factor of (x - 2)² - (x² - 4) ?

1. x + 2

2. x - 2

3. x²

4. x

Given,

Polynomial = (x - 2)² - (x² - 4)

= x² + 4 - 4x - (x² - 4)

= x² - x² + 4 + 4 - 4x

= -4x + 8

On substituting x = 2 in above polynomial, we get remainder :

= -4(2) + 8 = -8 + 8 = 0.

So, (x - 2) is a factor of (x - 2)² - (x² - 4).

Hence, Option 2 is the correct option.