factor by grouping. there are common terms among the first two terms and the last two terms of the original cubicf(x)=x^3+4x^2+9x+36
by the rational roots theorem (look it up), if there are rational roots to this equation, they will be from the factors of 24 (namely, ). start with the ones and plug them in and see if you get zero. if you obtain 0 for one, then it means that is a root. you can repeat this process with the others. or you may prefer to use polynomial long division or synthetic division to break down the polynomial in the following way.f(x)=x^4+x^3-2x^2+4x-24
let be one of the roots you found using the above method. so is a root. by the factor theorem, is a factor of the equation. so use long (or synthetic) division to compute
you will obtain a cubic as the result. for which you can repeat the process (or perhaps factoring by grouping can work). this way you keep breaking it down until you get to a quadratic, where factoring (i hope) is easy for you.
try them, good luck. if you don't understand something, say so