Question

Which one of the following statements is correct?

• A. If $x^6+1$ is divided by $x+1$, then the remainder is $-2$
• B. If $x^6+1$ is divided by $x-1$, then the remainder is $2$
• C. If $x^6+1$ is divided by $x+1$, then the remainder is $1$
• D. If $x^6+1$ is divided by $x-1$, then the remainder is $-1$

Answer 1

The correct option is B If $x^6+1$ is divided by $x-1$, then the remainder is $2$

By the remainder theorem,

If $(x-\alpha )$ divides $f\left(x\right)$ then $f\left(\alpha \right)$ is the remainder.
$\therefore$ if $x^6+1$ is divided by $(x-1)$ then,

Remainder $=f\left(1\right)=1^6+1$

$=2$