8. The inequality $x^{2}+p x>4 x+p-3$ holds for all $0 \leqslant p \leqslant 4$. Then the range of real numbers $x$ is $\qquad$ .
8. $x3$.

Hint: Convert the original inequality into a linear inequality about $p$ to get $p(x-1)+x^{2}-4 x+3>0$. Let $f(p)=p(x-1)+x^{2}-4 x+3$.
Then we only need $\left\{\begin{array}{l}f(0)>0, \\ f(4)>0 .\end{array}\right.$