9. Find the polynomial of least degree, having integral coefficients and leading coefficient equal to 1 , with $\sqrt{3}-\sqrt{2}$ as a zero.
9. $x^{4}-10 x^{2}+1$
We let $x=\sqrt{3}-\sqrt{2}$. We find the monic polynomial equation of least degree in terms of $x$. Squaring, we get
$$
x^{2}=(\sqrt{3}-\sqrt{2})^{2}=5-2 \sqrt{6} \quad \text { or } \quad x^{2}-5=-2 \sqrt{6} .
$$

Squaring the last equation, we finally get
$$
\left(x^{2}-5\right)^{2}=(-2 \sqrt{6})^{2} \text { or } \quad x^{4}-10 x^{2}+1=0 \text {. }
$$