Write the cubic in standard form: (ax^3+bx^2+cx+d)
Find a possible rational root using the Rational Root Theorem
Test each candidate by substitution or synthetic division
If (f(r)=0), then ((x-r)) is a factor
Divide the cubic by ((x-r)) using polynomial division or synthetic division
Factor the resulting quadratic, if possible
Write the full factorisation as ((x-r)(text{quadratic factor}))
If the quadratic does not factor nicely, use the quadratic formula
Check by expanding the factors to confirm the original cubic