Question 460856
{{{-x^3-x^2-x>0}}},multiply by -1 and reverse the sign of the inequality:

{{{x^3+x^2+x<0}}}, factor out x; {{{x(x^2+x+1)<0}}}. The quadratic polynomial

{{{x^2+x+1}}} is always positive because its discriminant is negative.

Therefore the product {{{x(x^2+x+1)}}} is negative when x<0.

Answer:The solution set of this inequality is { x| x<0 }.