Question 458709
Applying the rational root theorem, possible rational roots are -6, -3,-2, -1, 1,2,3,6.
Using the remainder theorem (or synthetic division), trying out x = -2:

{{{(-2)^3 + 2(-2)^2 + 3(-2) + 6 = 0}}}  Hence x = -2 is a rational root.  After synthetic division, the quotient is {{{x^2 + 3}}}, which doesn't even have real roots.