Question

10. (x+1) is a factor of x" +1 only if
(a) n is an odd integer
(c) nis a negative integer
(b) nis an even integer
(d) nis a positive integer​

Answer 1

Given,

$( x + 1) \: is \: a \: factor \: of \: ( {x}^{n} + 1$)

We have know that,

Euclid lemma of division

A = Bq + r

where, r = reminder

q = quotient

So,

xⁿ+1 = (x+1)q + 0

=> xⁿ+1 = (x+1)q

Put (x = -1)

then, -1ⁿ+1 = 0

=> -1ⁿ = -1

=>(means “n” must be an odd integer) .

So,

Option:-(a) n is an odd integer .

Hope it's helpful to you.