# Use remainder theorem to find the value of k, it being given that when

Question:

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

Solution:

Let $p(x)=x^{3}+2 x^{2}+k x+3$

Now, $p(3)=(3)^{3}+2(3)^{2}+3 k+3$

$=27+18+3 k+3$

$=48+3 k$

It is given that the remainder is 21

$\therefore 3 k+48=21$

$\Rightarrow 3 k=-27$

$\Rightarrow k=-9$