Question

26. Use factor theorem to prove that (x + a) is a factor of (x" +a") for any odd
positive integer n.

Please solve this question

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Answer 1

proved that (x + a) is a factor of (x" +a") for any odd positive integer n.

Answer 2

Correct question: Use the factor theorem to prove that x+a is a factor of $x^n+a^n$ for any odd positive integer n

Answer:

Step-by-step explanation:

Given Problem:

Use the factor theorem to prove that x+a is a factor of $x^n+a^n$ for any odd positive integer n

There are some errors in our question!This questionis correct!

Solution:

Let p(x) = $x^n+a^n$

The zero of $x+a \ is - a | x+a  = 0 => - a$

Now,

$p (-a) = (-a)^n +a^n = (-1)^n a ^n+a^n$

$=(-1)a^n+a^n$

$= n \ is \ an \ odd \ positive \ integer$

$=>(-1)^n = -1$

$=>- a^n+a^n = 0$

By Factor therem,x+a is a factor of $x^n +a^n$ for any odd positive integer n.