Let <i> p</i> be a prime and suppose that <i> f(x)</i> belongs to <i> Z[x]</i> with <I>deg f(x) &#8805 1</I>.
Let <i>f*(x)</I> be the polynomial in <i>Z<sub>p</sub>[x]</I> obtained from <i>f(x)</i> by reducing
all the coefficients of <i>f(x)</i> modulo <i>p</I>. If <i>f*(x)</i> is irreducible over <i> Z<sub>p</sub></i> and
<i>deg f*(x) = deg f(x)</i>, then <i>f(x)</i> is
irreducible over <i>Q.</i>