I did not understand the highlighted sentence of the exercise below:
My question is: how does it follow that $f(x)=0$ has a solution mod $p$ implies that $f(x)$ (mod $p$) splits as the product of linear factors in $\Bbb{Z}/p\Bbb{Z}$, i.e has all the roots in $\Bbb{Z}/p\Bbb{Z}$?