Let $f$ be a polynomial in $k[x,y,z]$. I want to know if it is irreducible. Does it suffice to show that $f$ is irreducible in
- $k[x,y][z]$, the polynomial ring in one variable over $k[x,y]$
- $k[x,z][y]$, the polynomial ring in one variable over $k[x,z]$
- $k[y,z][x]$, the polynomial ring in one variable over $k[y,z]$
If so, how is this proven?