Question

The remainder when $x^{31}+31$ is divided by $x+1$ is :

• A. $30$
• B. $31$
• C. $-1$
• D. $0$

Answer 1

The correct option is A $30$

For finding the remainder, we need to use remainder theorom

let $p\left(x\right)=x^{31}+31$
x6−2x5+3x2+4
x3−2x2+x+1

Hence, to find the remainder on dividing $p\left(x\right)$ by $x+1$, we need to equate $x+1$ to $0$ and put that value of $x$ in $p\left(x\right)$.

$x+1=0$

$\therefore x=-1$

$p(-1)={(-1)}^{31}+31=30$

Thus $x^{31}+31$ leaves remainder $30$ when divided by $x+1$

Hence option $A$ is correct