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.
Try to factorize \(x^7 + x^2 + 1\).
Observe that \(\omega\) and \(\omega^2 \) are the roots of \(x^7 + x^2 + 1\).
\(x^7 + x^2 + 1\) = (\(x^2 + x + 1\)).(\(x^5 – x^4 + x^2 -x + 1\))
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