Question

f(x) = x^n + a^n is divided by x+a​

Answer 1

$\huge\fcolorbox{aqua}{cyan}{\huge\underline{Answer}}$

.Let f(x) = x + a^n.

In order to prove that x+a is a factor of f(x)

for any odd positive integer n, it is sufficient

to show that f(-a) = 0.

f(-a) = (-a)n + an = (-1)^na^n + a^n

f(-a) = (-1+1)a^n [n is odd positive

integer]

f(-a) = 0 x a^n = 0

Hence, x + a is a factor of x^n + a^n, when nis

an odd positive integer.