Q:

Methods of polynomials division

How does the division method for polynomial discovered.  I have read about ruffini method, it needs divisor to be binomial and linear, I tried to understand horner's method, but couldn't.  but methods are traditional and different from what I am doing (like this one below):

How this method (image one) came from earlier methods? 

A:

I like the following way:
$$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$

