A polynomial   <i>f</i>(<i>x</i>) in <I>F</I>[<I>x</I>]
  splits in <I>E</i>
it     can be factored as a product of linear factors in
an  <I>E</I>[<I>x</I>],
where  <I>E</I> is an extension field of
<I>F</I>.