1957 AHSME Problem 29

The relation x^2(x^2 - 1)\ge 0 is true only for:

\begin{array}{l} \textbf{(A)}\ x \ge 1\qquad \textbf{(B)}\ - 1 \le x \le 1\qquad \textbf{(C)}\ x = 0,\, x = 1,\, x = - 1\qquad \\\textbf{(D)}\ x = 0,\, x\le-1,\, x\ge 1\qquad\textbf{(E)}\ x\ge 0 \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.