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Use factor theorem to verify that x+a is actore of x^n + a^n for any old positive integer?
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Use factor theorem to verify that x+a is actore of x^n + a^n for any o...
Let p(x) = x^n + a^n
The zero of x + a is - a. | x + a = 0 ⇒ x = - a
Now,
p(- a) = (- a)^n + a^n = (- 1)^na^n + a^n
= (- 1)a^n + a^n 
    
because n is an odd positive interger
therefore   (-1)^n = - 1
= - a^n + a^n = 0
∴ By Factor Theorem, x + a is a factor of x^n + a^n for any odd positive integer n.
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Use factor theorem to verify that x+a is actore of x^n + a^n for any old positive integer?
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