Question:medium

If \( f(x) \) and \( g(x) \) are polynomials such that \[ \phi(x) = f(x^3) + xg(x^3) \] is divisible by \( x^2 + x + 1 \), then:

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For divisibility by cyclotomic polynomials: \begin{itemize} \item Substitute complex roots. \item Use symmetry relations. \end{itemize}

Updated On: Mar 2, 2026

\( \phi(x) \) divisible by \( x-1 \)
none divisible by \( x-1 \)
\( g(x) \) divisible by \( x-1 \), \( f(x) \) not
\( f(x) \) divisible by \( x-1 \), \( g(x) \) not

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The Correct Option is D

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