Question

Solve the polynomial inequality

x^2+5x >or= -6

(-infinity, -3]u [-2, infinity)

or [-3,-2]

Answer 1

x^2+5x >or= -6 or
x^2 + 5x + 6 ≥ 0
(x+2)(x+3) ≥ 0

the critical values are x = -2, x= -3

if we consider y = x^2 + 5x + 6 we have a parabola which opens upwards and crosses the x-axis at -2 and -3
so it will be above the x-axis (or ≥ 0 )
for

x ≤ -3 OR x ≥-2

I suppose your notation of (-infinity, -3]u [-2, infinity) means the same thing, it just looks quite awkward.