Question

$(x{)}^n+(a{)}^n$ is completely divisible by $x+a$, then $n$ can be

• A. $7028$
• B. $861$
• C. $26$
• D. $782$

Answer 1

Answer: (B)

$861$

By remainder theorem,

$f\left(x\right)=x^n+a^n$ is divisible by $x+a$, if $f(-a)=0$
$\Rightarrow (-a{)}^n+a^n=0$
This is only possible if $n$ is odd.