What is the difference between trivial and non-trivial GCDs of two polynomials: $f,g$ where $f,g \in Q[x]$? I know if $f,g \in Z[x]$, the only non-trivial GCD is 1, and everything else is trivial. Does this also apply for Q[x]?
2026-04-11 14:10:52.1775916652
Trivial and nontrivial GCD of polynomials
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Since all $a\in \Bbb Q\setminus\{0\}$ are units in $\Bbb Q[x]$, the trivial GCD's in $\Bbb Q[x]$ are the non-zero constants.