Question

use the factor theorem to prove that (x+a) is a factor of (x^n+a^a) for any odd positive integer n

Answer 1

Correction in question it is (x^n+a^n)

Let p(x) = x^n + a^n , where n is odd positive integer.
Take (x+a)= 0
=> x = -a

Consider:
p(-a) = (-a) ^n + (a) ^n
= -a^n + a^n
= 0
Since, n is odd.

By Factor theorem,
(x+a) is a factor of p(x) when n is odd positive integer.

Answer 2

Answer:Correction in question it is (x^n+a^n)

Let p(x) = x^n + a^n , where n is odd positive integer.

Take (x+a)= 0

=> x = -a

Consider:

p(-a) = (-a) ^n + (a) ^n

= -a^n + a^n

= 0

Since, n is odd.

By Factor theorem,

(x+a) is a factor of p(x) when n is odd positive integer .

Step-by-step explanation: