Construct a quartic polynomial with integer coefficients, one of whose roots is [math]\sqrt{5}-\sqrt{2}[/math].

If [math]\sqrt{5}-\sqrt{2}[/math] is a root, then [math]\sqrt{5}+\sqrt{2}[/math] is a root. Also, [math]-\sqrt{5}-\sqrt{2}[/math] and [math]-\sqrt{5}+\sqrt{2}[/math] are roots as well. With 4 roots, we can now construct a quartic polynomial. [br]([math]x-\sqrt{5}-\sqrt{2}[/math])([math]x-\sqrt{5}+\sqrt{2}[/math])([math]x+\sqrt{5}+\sqrt{2}[/math])([math]x+\sqrt{5}-\sqrt{2}[/math]).