Synthetic Division

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Synthetic division is a method of performing polynomial long division, with less writing and fewer calculations. It is mostly taught for division by binomials of the form x - a, but the method generalizes to division by any monic polynomial. This method can be used instead of long division on integers by considering 10 = x and only substituting 10 back in at the end. The most useful aspect of synthetic division is that it allows one to calculate without writing variables using fewer calculations. As well, it takes significantly less space than long division. Most importantly, the subtractions in long division are converted to additions by switching the signs at the very beginning, preventing sign errors.