Question

If $(x+1)$ is a factor of $x^n+1$, which of the following statements is true?

• A. n is an odd integer
• B. n is an even integer
• C. n is a negative integer
• D. n is a positive integer

Answer 1

The correct option is A n is an odd integer

If $n$ is odd then $x^n+1$ is zero at $-1$

So $x=-1$ i.e $(x+1)$ is always a factor of $x^n+1$ if $n$ is an odd integer.

Hence, option A is correct.