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**Algebraicgeometry421** Hello, I am trying to show that y^5 -x^2 is irreducible in R[x,y]. (R represents the set of real numbers and R[x,y] , the polynomial ring in two variables)

I have tried everything but still don't know how to show this!

Here's what I tried:

y^5 -x^2 = fg , where f&g are non constant polynomials in R[x,y].

Then let x=t^5 and y=t^2.

so, 0=f(t^5,t^2)g(t^5,t^2), which implies

either f(t^5,t^2)=0 or......

My professor said this is the best approach and I should find a contradiction.

Any help will be grateful thanks.