x^3+6x^2+20x+24
looks like we are factoring, ....
let f(x) = x^3+6x^2+20x+24
try x = ±1, ±2, ±3 , ±4 , ± 6, ± 8
on the 4th try:
f(-2) = -8 + 24 - 40 + 24 = 0
so x+2 is a factor
using either synthetic or long algebraic division we get
x^3+6x^2+20x+24 = (x+2)(x^2 + 4x + 12)