Use factor theorem to verify that x+a is factor of xn+an for any odd positive integer
Attachments:
Answers
Answered by
0
Answer:
Use factor theorem to verify that x+a is a factor of xn+an for nay odd positive integer. Let f(x)=xn+an. 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.
Answered by
5
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:
Similar questions