Question

If $x^{31}+31$ is divided by $byx+1$, then what will be the remainder?

Answer 1

Let $f\left(x\right)=x^{31}+31$.

Now according to the remainder theorem the remainder when $f\left(x\right)$ is divisible by $(x+1)$ is $f(-1)$ and it is $-1+31=30$.