If you want to solve a series of synthetic division exercises and need a little help, you have come to the right place. The Synthetic Division Calculator is an excellent tool to study and understand this polynomial division technique based on Ruffini’s rule.
To use the polynomial synthetic division calculator you just have to follow these steps:
Here is an explanation of the synthetic division method or Ruffini’s rule.
Synthetic division is a simplified method of dividing polynomials. This method is also called division by Ruffini’s rule, since today we can make use of this magnificent method thanks to the study carried out by Paolo Ruffini in the 19th century for divisions of polynomials in which the divisor is of the form x±k.
The synthetic division method ignores the variables, thus focusing on the coefficients. It is important to note that it is possible to use the ruffini rule for divisions in which the divisor is of a higher degree than unity (the synthetic division calculator can do it), but to be more practical in the rest of this article we will focus on the case of a linear divider.
To perform synthetic division, you need to have a polynomial and a linear expression in the form of (x – a). The polynomial should be written in descending order of the exponents, and the linear expression should be written as the divisor.
To divide the polynomial by the linear expression, you follow these steps:
Write the coefficients of the polynomial in a row, starting with the coefficient of the term with the highest exponent.
Write the linear expression as the divisor, with a blank space below it.
In the first blank space below the divisor, write the coefficient of the term with the highest exponent in the polynomial.
Multiply the coefficient in the divisor by the coefficient in the first blank space and write the result in the second blank space.
Add the result in the second blank space to the coefficient in the second blank space in the polynomial. Write the result in the third blank space.
Repeat this process until you have filled all the blank spaces.
We will clearly explain how to divide polynomials by the synthetic division method by presenting the following example:
x2-x+10 – 24/(x+3)