Late last year I applied to Wolfram Research for a position in the development of Wolfram|Alpha for education. The applicants were given a coding problem set. One of them was to create a function which shows step-by-step work. Obviously by the title of this thread, I chose to do one for General Synthetic Division.

That is, for those who are not aware, you can use synthetic division to perform division on polynomials that your teachers told you that you must use long division for, as "synthetic division is only for when dividing by a binomial with the coefficient of x being 1".

This is a brief (silent) video showing a demonstration.

And here is the Notebook. (I minimized the code, but obviously you can maximize it to view it.)

According to my knowledge, it can divide any two polynomials and shows all of the work. (It's color-coded as well!)

Enjoy!

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