MCQ
$(x + 1)$ is a factor of $x^n+1$ only if:
- ✓$n$ is an odd integer
- B$n$ is an even integer
- C$n$ is a negative integer
- D$n$ is a positive integer
✓
Answer
Correct option: A.
$n$ is an odd integer
If $x+1$ is a factor of $x^n+1$
then, at $x=-1, x^n+1=0$
$(-1)^n+1=0$
$(-1)^n=-1$
$(-1)^{\mathrm{n}}$ will be equal to $-1$ if and only if $n$ is an odd integer.
If $n$ is even, then $(-1)^{\mathrm{n}}=1$
So, $n$ should be an odd integer.
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