a) Prove that the polynomial $\displaystyle f(X)=X^3-6X^2+9X+3$ is irreducible over $\displaystyle Q$

b) Consider the extension $\displaystyle Q \subset Q(u)$ where $\displaystyle u$ is a real root of $\displaystyle f$. Express $\displaystyle u^4$ and $\displaystyle (u+1)^{-1}$ like a linear combination of elements from the basis $\displaystyle \{1,u,u^2\}$.

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