The standard form of a cubic polynomial with the leading coefficient equal to 1 is f(z) = z^3 + az^2 + bz + c.  This is usually transformed to a reduced form by means of a substitution z = x - a/3.  Let's see how this works:

f(x - a/3) = (x - a/3)^3 + a(x - a/3)^2 + b(x - a/3) + c
  = x^3 - 3ax^2/3 + 3a^2x/9 - a^3/27 + ax^2 - 2a^2x/3 + a^3/9 + bx - ab/3 + c
  = x^3 + (b - a^2/3)x + (2a^3/27 - ab/3 + c)
  = x^3 - mx - n,

replacing an equation f(z) = 0  with a depressed cubic equation x^3 = mx + n.


Cubic Formula