Question

Use factor theorem to verify that (x+a) is a factor of x ki power n + A ki power n for any odd positive integer

Answer 1

Let f (x)=x^n + a^n
x+a will be the factor of f(x), if f (-a)=0
Now, f (-a) = (-a)^n + a^n=0 (since 'n' is a odd positive integer).
Thus, x+a is a factor of x^n+a^n.

Answer 2

Answer:

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: