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?
On
So you are asking how the long division that people usually use(i.e. the long division) was derived or infered from the simple ones such as the ruffini method. I'm not sure but you could show that ruffini method is special case of the long division. here is a youtube video showing how they are related for a special case.
I like the following way: $$2x^3-7x^2+11=2x^3-6x^2-x^2+3x-3x+9+2=(x-3)(2x^2-x-3)+2.$$