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Use factor theorem to prove that (x+a) ...

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

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Let `p(x)=(x^(n)+a^(n))`, where n is any odd positive integer.
Let `g(x)=x+a. "Then", g (x) = 0 rArrx+a=0rArrx=-a`.
Now , `p(-a)={(-a)^(n)+a^(n)}={(-1)^(n)a^(n)+a^(n)}={(-1)^(n)+1}a^(n)`
`=(-1+1)a^(n)=0` " " `[becausen " being odd", (-1)^(n)=-1]`.
By factor theorem , ( x+a ) is a factor of `(x^(n)+a^(n))` , when n is an odd positive integer.
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