Question
$(x + 1)$ is a factor of $x^n + 1$ only if:
✓
Answer
If $x + 1$ is a factor of $x^n + 1,$
then, at $x = -1, x^n + 1 = 0$
$(-1)^n + 1 = 0$
$(-1)^n = -1$
$(-1)^n$ will be equal to $-1$ if and only if $n$ is an odd integer.
If $n$ is even, then $(-1)^n = 1$
So, $n$ should be an odd integer.
then, at $x = -1, x^n + 1 = 0$
$(-1)^n + 1 = 0$
$(-1)^n = -1$
$(-1)^n$ will be equal to $-1$ if and only if $n$ is an odd integer.
If $n$ is even, then $(-1)^n = 1$
So, $n$ should be an odd integer.
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