Question

When $x^{13}+1$ is divided by $x-1$, the remainder is

• A. $1$
• B. $-1$
• C. $0$
• D. $2$
• E. None of these

Answer 1

The correct option is D $2$

By remainder theorem, if $f\left(x\right)$ is divided with $x-a$, then the remainder will be $f\left(a\right)$.
Given polynomial dividend $f\left(x\right)=x^{13}+1$.
Divisor $=x-1⟹a=1$
Remainder $=f\left(1\right)=1^{13}+1=2$