(x + 1) is a factor of xn + 1 only if: - Vidyadip

MCQ

(x + 1) is a factor of xⁿ + 1 only if:

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

n is an odd integer
Solution:
If x + 1 is a factor of xⁿ + 1,
then, at x = -1, xⁿ + 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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