Identify the equation as a cubic: (ax^3 + bx^2 + cx + d = 0)
Look for a greatest common factor and factor it out first
Group terms if possible and factor by grouping
Use the Rational Root Theorem to test possible rational roots
Substitute a found root (r) into ((x-r))
Divide the cubic by ((x-r)) using synthetic division or polynomial long division
Factor the resulting quadratic if possible
Write the full factorization as ((x-r)(text{quadratic factor}))
If the cubic matches a special form, use identities such as (a^3-b^3=(a-b)(a^2+ab+b^2))
If the cubic is a sum of cubes, use (a^3+b^3=(a+b)(a^2-ab+b^2))
If no rational factor exists, use numerical methods or the cubic formula to find roots