The polynomial \(x^7+x^2+1\) is divisible by

  • (A) \(x^5-x^4+x^2-x+1\) (B) \(x^5-x^4+x^2+1\)
  • (C) \(x^5+x^4+x^2+x+1\) (D) \(x^5-x^4+x^2+x+1\)

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Understanding the Problem:

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We will guide you along a short path to the solution in a step by step approach.

Hint 1:


Try to factorize \(x^7 + x^2 + 1\).


Hint 2:


Observe that \(\omega\) and \(\omega^2 \) are the roots of \(x^7 + x^2 + 1\).


Hint 3:


\(x^7 + x^2 + 1\) = (\(x^2 + x + 1\)).(\(x^5 – x^4 + x^2 -x + 1\))



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