Question-3 Show that x + a is a factor of x n +a n for any odd +ve integer n .

Question

Question-3 Show that x + a is a factor of  x n +a n for any odd +ve integer n .

Philoid · Accepted Answer

Let f(x) = xⁿ + aⁿ
x + a will be the factor of xⁿ +aⁿ if f(-a) = 0
Now f(- a) = (- a)ⁿ+ aⁿ= 0 (since n is a odd +ve integer)
Thus (x + a) is a factor of xⁿ + aⁿ.

Question-3 Show that x + a is a factor of xn +an for any odd +ve integer n.

Question-3 Show that x + a is a factor of xⁿ+aⁿ for any odd +ve integer n.