Moderate# Polynomial Rings:Properties $F[x,y]$ shares with $F[x]$,$F$ field

ABSALG-PWFFCD

Let $F$ be a field, let $F[x]$ be the ring of polynomials in one variable $x$ with coefficients in $F$, and let $F[x,y]$ be the ring of polynomials in two variables $x$, $y$ with coefficients in $F$.

Below, we list some true properties of the ring $F[x]$. Select **all the complete sentences** that describe properties of $F[x]$ that **are not shared** by $F[x,y]$.

$F[x]$ is an Integral Domain.
$F[x]$ is a Unique Factorization Domain.
$F[x]$ is a Principal Ideal Domain.
$F[x]$ is a Euclidean Domain.
The units of $F[x]$ are the nonzero constant polynomials.