Problem

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:

The problem is easy to understand right?

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STOP

Before scrolling down, your first task is to try the problem YOURSELF.

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

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Hint 1:

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

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Hint 2:

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

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Hint 3:

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

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