(i) p(x) = x² + x + k
Putting x – 1 = 0, we get, x = 1
Using remainder theorem, when p(x) = x² + x + k is divided by x – 1, remainder is given by p(1)
= (1)² + (1) + k
= 2 + k
Since x – 1 is a factor of p(x), hence remainder p(1) = 0
⇒ 2 + k = 0
⇒ k = -2