Problem:
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}.
Provide complete and step by step solution for the question and show calculations and use formulas.