Question

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

• A. $P\left(x\right)$ is divisible by $(x-1)$ but $Q\left(x\right)$ is not divisible by $(x-1)$
• B. $Q\left(x\right)$ is divisible by $(x-1)$ but $P\left(x\right)$ is not divisible by $(x-1)$
• C. Both $P\left(x\right)$ and $Q\left(x\right)$ are divisible by $(x-1)$
• D. $f\left(x\right)$ is divisible by $(x-1)$

Answer 1

The correct option is D $f\left(x\right)$ is divisible by $(x-1)$