Question

Is x^4-1 a factor of P(x)=x^5+5x^4-x-5

Answer 1

Answer:

  yes

Step-by-step explanation:

The other factor is (x+5), so the product is ...

  (x^4 -1)(x +5) = x^5 +5x^4 -x -5 = P(x)

(x^4 -1) is a factor of P(x).

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It is not a primitive factor, because it can be factored as ...

  x^4 -1 = (x^2 -1)(x^2 +1) = (x -1)(x +1)(x^2 +1)

The complete factorization of P(x) to real numbers is ...

  P(x) = (x -1)(x +1)(x +5)(x^2 +1)