# How did Ruffini discover his method of polynomial division?

How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?

Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $$10$$, so he may well be the first to provide a mathematical justification for a positional division algorithm.