Question

The sum of remainder obtained when $x^3+(k+8)x+k$ is divided by $x-2$ and when it is divided by $x+1$ is $0$ find the value of $K$.

Answer 1

$x^3+(k+8)x+k$

Put $x=2$ to obtain first remainder

$\Rightarrow R_1=(2{)}^3+(k+8{)}^2+k=24+3k$

Put $x=-1$ to obtain second remainder

$\Rightarrow R_2=(-1{)}^3+(k+8)+k=-9$

So $R_1+R_2=0$

$\Rightarrow 24+3k-9=0$

$\Rightarrow 3k=-15$

$\Rightarrow k=-5$.