Difficult: I don't understand extension fields very well. I understand what they are, but I don't understand why a polynomial that doesn't have a root in F[x]/p(x) can have a root in the extension field K. I also don't understand what the use of this extension field will be.
Reflective: While I don't understand extension fields, I think it will be interesting to learn about them and understand how they work and how they will be used. I also am interested by the fact that an extension field K is isomorphic to the complex numbers C.
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