Answer
(-∞, -4] U [-2, 1] U [3, ∞)
Work Step by Step
$(x-1)(x+2)(x -3) (x+4) \geq 0$
Find the roots of the function
$x = -4, -2, 1, 3$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -4] $(-)(-)(-)(-) = (+)$
[-4, -2] $(-)(-)(-)(+) = (-)$
[-2, 1] $(-)(+)(-)(+) = (+)$
[1,3] $ (+)(+)(-)(+) = (-) $
[3, ∞) $(+)(+)(+)(+) = (+)$
Thus the solution is (-∞, -4] U [-2, 1] U [3, ∞)
