Answer
$(-∞, -2] U [2, 3] $
Work Step by Step
$x^3 - 3x^2 - 4x + 12 \leq 0$
Find the zeros of the expression.
$x^2 (x - 3) - 4 (x - 3)$
$(x^2 - 4) (x - 3)$
$(x+2)(x-2) (x-3)$
$x = -2, 2, 3$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -2] $(-)(-)(-) = (-)$
[-2, 2] $(+)(-)(-) = (+)$
[2, 3] $(+)(+)(-) = (-)$
[3, ∞) $(+)(+)(+)= (+)$
Thus the solution is $(-∞, -2] U [2, 3] $