Let <I>F</I> be a field and let
 <i>f</i>(<i>x</i>)
  be a nonconstant element of
 <I>F</I>[<I>x</I>].
 Does there always exist  a splitting field <i>E</I> for
 <i>f</i>(<i>x</i>)  over <I>F</i>?