The number $p-$ is a root of the cubic equation $x^{3}+x-3=0$.

Come up with a cubic equation with integer coefficients, for which the number $p^{2}$ is a root.

#
From the condition, it follows that $p^{3}+p=3$. Therefore, $\left(p^{3}+p\right)^{2}=9 \Leftrightarrow p^{6}+2 p^{4}+p^{2}-9=0$. Thus, $p^{2}$ is a root of the equation $x^{3}+2 x^{2}+x-9=0$.

## Answer

$x^{3}+2 x^{2}+x-9=0$