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20

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

Let us assume,

p (x) = x^{3} + 2x^{2} + 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