# Solve the polynomial inequality graphically. x^{3}-x^{2}-2xgeq0

Solve the polynomial inequality graphically. ${x}^{3}-{x}^{2}-2x\ge 0$
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Ayesha Gomez

We graph the left-hand side of the inequality and find that the x-intercepts are $x=-1,x=0,x=2$:

We find the intervals in the graph where $y\ge 0$. The solution to the inequality is $x\in \left[-1,0\right]\cup \left[2,\mathrm{\infty }\right)$