If (x - a) is a factor of f(x) then the remainder when f(x) - k is divided by (x - a) is :

1. 0

2. k

3. -k

4. a

By factor theorem,

If x - a is a factor of polynomial f(x), then remainder f(a) = 0.

Given,

(x - a) is a factor of f(x), then f(a) = 0.

Substituting x = a, in f(x) - k,

⇒ f(a) - k

⇒ 0 - k

⇒ -k.

Hence, Option 3 is the correct option.