This is an exercise from Dummit and Foote where the following hint is also given : $\mathbf{(K[X])(Y)=(K[Y])(X)}$. Does this mean that we can consider our polynomial over $\mathbf K[Y]$ with variable X now which will imply that it is irreducible being a linear polynomial and hence irreducible in the required field $\mathbf K(X)$? If I have misunderstood please guide me through the next step.
2026-03-26 13:51:38.1774533098
irreducibility of polynomial over field of rational functions
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