Question

6. Without actual division, prove that the
polynomial g(x) = x + a is a factor of the
polynomial f(x) = x^5 +a^5.​

Answer 1

Answer:

Refer the pic

Explanation:

hope it helps

Answer 2

It can be proved by the remainder theorem.

If g(x) = x + a is a factor of f(x) then f(-a) must be equal to zero.

So, f(-a) = (-a) ^5 + (a)^5

=> -a^5 + a^5

=> 0

Therefore, g(x) is a factor of f(x).

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