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Polynomial Division and Remainder Theorem - Class IX

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Multiple Choice

If $P(x)$ and $Q(x)$ are two polynomial such that $f(x)=P(x^3)+Q(x^3)$ is divisible by $x^2+x+1$, then?

  1. $P(x)$ is divisible by $(z-1)$ by $Q(x)$ is not divisible by $(x-1)$
  2. $Q(x)$ is divisible by $(x-1)$ but $P(x)$ is not divisible by $(x-1)$
  3. Both $P(x)$ and $Q(x)$ are divisible by $(x-1)$
  4. $f(x)$ is divisible by $(x-1)$
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