Please help and explain: x^3-4x greater than or equal to 0

x^3-4x greater than or equal to 0


has 4 intervals to be checked.
Because we are comparing the value to 0 we only need to know what its sign will be (why?)
on [-oo,-2] the signs are (-)(-)(-) -> (-) so false
on [-2,0] the signs are (-)(+)(-) -> (+) so true
on [0,2] the signs are (+)(+)(-) -> (-) so false
on [2, oo] the signs are (+)(+)(+) -> (+) so true
solution:
[-2,0]U[2,oo]