Solving polynomial inequalities- Z^3 + 7z^2 + 10z > 0
when is it zero (cross x axis?)
z (z^2 +7 z +10) = 0
z (z+2)(z+5) =0
so
at z = 0 , z = -2 , z=-5
if z<-5 try z = -6
-6(-4)(-1) is -24 so NO
then between -5 and -2 try -3
-3(-1)(2) = +6 so YES
between -1 and 0 try -.5
-.5(1.5)(4.5) = - so NO
bigger than 0, try +1
1(3)(6) = 18 so YES