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.