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