Answer
(a) $\{-2, 4, 1 \}$
(b) $(-\infty,-2)U(1,4)$
(c) $(-2,1)U(4,\infty)$
Work Step by Step
(a) Graph the function $f(x)=x^3-3x^2-6x+8$ as shown in the figure. We can identify the zeros as $x=-2,4, 1$ or $\{-2, 4, 1 \}$
(b) For $f(x)\lt 0$, we can identify the intervals as $(-\infty,-2)U(1,4)$
(c) For $f(x)\gt 0$, we can identify the intervals as $(-2,1)U(4,\infty)$
