Question

If (x − a) is a factor off(x) then the remainder when f(x) - k is divided by (x − a) is ______.

Options

• 0

• k

• −k

• a

Answer 1

If (x − a) is a factor off(x) then the remainder when f(x) - k is divided by (x − a) is −k.

Explanation:

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.