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    Polynomial rings

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    Consider the polynomial ring R=Q[x].

    (a) show that I = {f(x) (x^3-6x+7)+g(x) (x+4) | f(x), g(x) in R} is an ideal of R.

    (b) We have seen that R is a principle ideal domain. That is, every ideal is generated by a single element of R. Find h(x) in R so that I = {f(x)h(x) | f(x) in R}.

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    Solution Summary

    This solution provides step by step explanations for how to solve the given problem involving polynomial rings.