Let $f(x,t)$ be a polynomial with coefficients from $\mathbb{Z}[x,t]$. I am wondering how to check for irreducibility of $f(x,t)$ over $\mathbb{Z}[t]$.
Any help is kindly acknowledged. Thank you
Asked
Active
Viewed 22 times
0
-
What sense does it make for a polynomial in $x$ and $t$ to have coefficients that are polynomials in $x$ and $t$? Did you just mean to write that the coefficients are integers? – Gerry Myerson Dec 19 '17 at 06:36
-
I was wondering some thing like $f(x,t)=a(t)x^2+b(t)x+c(t)$, where $ a(t), b(t), c(t) $ are from $Z[t]$ – Math123 Dec 19 '17 at 06:56
-
OK, but then that's what you should write. You could write $f$ is in $({\bf Z}[t])[x]$. But that's the same, isn't it, as saying $f$ is in ${\bf Z}[x,t]$, or just saying $f$ is a polynomial in $x$ and $t$ with integer coefficients, right? – Gerry Myerson Dec 19 '17 at 07:03
-
yes, got it. Thank you – Math123 Dec 19 '17 at 10:39