\[x^{3} - 4x^{2} + 8x - 32 \geq 0;\ \ \ \ x \geq 4\]
\[x^{2}(x - 4) + 8 \cdot (x - 4) \geq 0\]
\[(x - 4)\left( x^{2} + 8 \right) \geq 0\]
\[x^{2} + 8 > 0\ всегда;\ \ \]
\[x - 4 \geq 0 - из\ условия.\]