Find the remainder (without division) on dividing $f\left(x\right)$ by $(x-2)$where 
$f\left(x\right)=2x^3-7x^2+3$

Using the remainder theorem, find the remainders obtained when $x^3+(kx+8)x+k$ is divided by $x+1$ and $x-2$.

Hence, find $k$ if the sum of two remainders is $1$ .