Factor out the greatest common factor first
Look for grouping opportunities
Use the Rational Root Theorem to test possible rational zeros
Substitute a tested root into the polynomial
Use synthetic division or long division to divide by the corresponding linear factor
Rewrite the cubic as a product of a linear factor and a quadratic factor
Factor the quadratic factor if possible
Use special factoring patterns when applicable, such as sum or difference of cubes
Check the factorization by multiplying the factors back together