Is $(x^2-1)^2+(y^2-1)^2-1$ irreducible in $\mathbb{R}[x,y]$ ?
Is $(x^2-1)^2+(y^2-1)^2$ irreducible in $\mathbb{R}[x,y]$ ?
Are these polynomials irreducible in $\mathbb{R}[x,y]$?
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ring-theory
commutative-algebra
irreducible-polynomials
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11) $(y^2-1)^2-1=y^2(y-\sqrt 2)(y+\sqrt2)$ and Eisenstein. – 2017-02-01
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02) Use its decomposition in $\mathbb C[x,y]$. (Note that both polynomials you got are irreducible and not associate over $\mathbb C$.) – 2017-02-01