Question

Use remainder theorem to find the value of k, it being given that when x³ + 2x² + kx + 3 is divided by (x – 3) then the remainder is 21.

Answer 1

Given: f(x) = x³ + 2x² + kx + 3 and when f(x) is divided by (x – 3) the remainder is 21.

To Prove: Find the value of k.

Proof [Step-wise]:

1. By the Remainder Theorem, remainder = f(3).

2. Compute f(3):

f(3) = 3³ + 2 × 3² + 3k + 3 

= 27 + 18 + 3k + 3

= 48 + 3k

3. Set remainder equal to 21:

48 + 3k = 21

4. Solve: 3k = 21 – 48

= –27

⇒ k = −9