Let <i>a</i> be algebraic over <i>F</I> and let <I> p(x)</I>   be the minimal polynomial for <i>a</i> over <i>F</i>.  If <i> f(x)  &#8712 F[x]</i>  and <i>f(a) = 0 </i>, then <i>p(x)</i>  divides  <I>f(x)</i> in <I>F[x]</i>.