Answer
(a) $\{-5,-2, 3 \}$
(b) $(-\infty,-5)U(-2,3)$
(c) $(-5,-2)U(3,\infty)$
Work Step by Step
(a) Graph the function $f(x)=x^3+4x^2-11x-30$ as shown in the figure. We can identify the zeros as $x=-5,-2, 3$ or $\{-5,-2, 3 \}$
(b) For $f(x)\lt 0$, we can identify the intervals as $(-\infty,-5)U(-2,3)$
(c) For $f(x)\gt 0$, we can identify the intervals as $(-5,-2)U(3,\infty)$
