I need to calculate the sums
$x_1^3 + x_2^3 + x_3^3$
and
$x_1^4 + x_2^4 + x_3^4$
where $x_1, x_2, x_3$ are the roots of
$x^3+2x^2+3x+4=0$
using Viete's formulas.
I know that $x_1^2+x_2^2+x_3^2 = -2$, as I already calculated that, but I can't seem to get the cube of the roots. I've tried
$(x_1^2+x_2^2+x_3^2)(x_1+x_2+x_3)$
but that did work.