what are the roots of x^3+6x^2+12x+8?
cubics are tough. Look for low-hanging fruit. Clearly there are no positive roots, since all the coefficients are positive.
f(-1) = -1+6-12+8 = 1
f(-2) = -8+24-24+8 = 0
So, x^3+6x^2+12x+8 = (x+2)(x^2+4x+4)
Now it's easy