Question: For this problem, i need help with not only solving this problem in Abstract Algebra, but I also need a reflective narrative to describe all

For this problem, i need help with not only solving this problem in Abstract Algebra, but I also need a reflective narrative to describe all the methods and justifications for my proof as well. Please, please make it legible as I often have a very hard time being able to read the handwriting. Please make it as clear as possible, even if it takes more time.

6. Suppose that f(x) and g(x) are irreducible over F and that deg f(x) and deg g(x) are relatively prime. If a is a zero of f(x) in some extension of F, show that g(x) is irreducible over F(a).\f

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