(b) \( x(x-1)(x+5)>0 \) Use the tools to enter your answer.

To solve the inequality \( x(x-1)(x+5)>0 \), we need to identify the points where the expression equals zero. The critical points are found by setting each factor to zero: \( x = 0, x = 1, x = -5 \). The sign of the expression will change at these points, so we analyze the intervals created by these critical points: \( (-\infty, -5) \), \( (-5, 0) \), \( (0, 1) \), and \( (1, \infty) \). Choose a test point from each interval to determine the sign: - For \( x < -5 \) (e.g., \( x = -6 \)): \( (-)(-)(-) < 0 \). - For \( -5 < x < 0 \) (e.g., \( x = -1 \)): \( (-)(-)(+) > 0 \). - For \( 0 < x < 1 \) (e.g., \( x = 0.5 \)): \( (+)(-)(+) < 0 \). - For \( x > 1 \) (e.g., \( x = 2 \)): \( (+)(+)(+) > 0 \). Thus, the solution is the union of the intervals where the expression is greater than zero: \( (-5, 0) \cup (1, \infty) \).