Write the cubic in standard form: (ax^3+bx^2+cx+d)
Check for a greatest common factor and factor it out
Use the Rational Root Theorem to list possible rational roots
Test possible roots by substitution or synthetic division
If (r) is a root, factor out ((x-r))
Divide the cubic by ((x-r)) to get a quadratic
Factor the quadratic using standard methods
Write the full factorization as ((x-r)(text{quadratic factors}))
If no rational root exists, use numerical methods or the cubic formula
Verify the factorization by expanding the factors