The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.1663\\[1 em]x_2 &= 0.0832+1.5874i\\[1 em]x_3 &= 0.0832-1.5874i \end{aligned} $$Polynomial $ x^3+3x^2+2x+8 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.