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.

Let us assume,

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 in the question that the remainder is 21


Hence, 3k + 48 = 21


3k = - 27


k = - 9


20