find all ideals of quotient ring $Q[x]/I$ where $I = Q[x]f(x)$, $f(x) = x^3 + 4x^2-9x-36$.
should I first factor the $f(x)$? Are those Factors of $f(x)$ the ideal of $Q[x]/I$? Thanks
2026-03-26 21:09:16.1774559356
find all ideals of quotient ring $Q[x]/I$
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Yes, factor $f(x)$ and then use the correspondence theorem, which tells you that ideals of $\mathbb{Q}[x]/I$ are all of the form $J/I$, where $J$ is an ideal of $\mathbb{Q}[x]$ containing $I$.