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

Let p(x) = x³ + 2x² + kx + 3 

Now, p(3) = (3)³ + 2(3)² + 3k + 3 

= 27 + 18 + 3k + 3 

= 48 + 3k 

It is given that the reminder is 21 

∴ 3k + 48 = 21 

⇒3k = –27 

⇒ k = –9