In algebra, synthetic division is a method of performing Euclidean division of polynomials, with less writing and fewer calculations than occur with polynomial long division. It is mostly taught for division by binomials of the form
x
−
a
,
{\displaystyle x-a,\ }
but the method generalizes to division by any monic polynomial, and to any polynomial.
The advantages of synthetic division are that it allows one to calculate without writing variables, it uses few calculations, and it takes significantly less space on paper...