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.