Question 389989
{{{x^3 + x^2 - 2x < 0}}} ===> {{{x(x^2 + x - 2) < 0}}} ===> x(x+2)(x-1) < 0.  The critical numbers of the inequality are -2, 0, and 1.  They partition the real number line into 4 parts.  Use test numbers -3, -1, 0.5, and 2 in each respective part.  
For ({{{-infinity}}}, -2), x(x+2)(x-1) < 0.
For (-2,0), x(x+2)(x-1) > 0.
For (0,1), x(x+2)(x-1) < 0.
For (1, {{{infinity}}}), x(x+2)(x-1) > 0.
The solution set is then the union ({{{-infinity}}}, -2)U (0,1).