Question

If $x^n-1$ is divisible by $x-k$, then the least positive integral value of $k$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

if $f\left(x\right)=x^n-1$ is divisible by $x-k$

Then $f\left(k\right)=0$

Therefore, $k^n=1$

and thus least positive integral value of k is 1