Write the cubic in standard form: (ax^3+bx^2+cx+d)
Factor out the greatest common factor, if any
Use the Rational Root Theorem to list possible rational zeros
Test possible zeros by substitution or synthetic division
If a zero is found, divide the cubic by ((x-r))
Factor the resulting quadratic, if possible
Use grouping if the cubic has four terms or can be rearranged
Use special factoring patterns if applicable
Write the final answer as a product of linear factors and/or an irreducible quadratic
Check by multiplying the factors back together