Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. It is a simplified way of dividing polynomials with less effort of calculation than the long division method. The method is mostly taught for division by linear monic polynomials, but it can be generalized to division by 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 than long division. The subtractions in long division are converted to additions by switching the signs at the very beginning, helping to prevent sign errors.

The synthetic division method is performed manually with less effort of calculation than the long division method. Usually, a binomial term is used as a divisor in this method, such as x – b. The requirements of the synthetic division method are that the divisor of the polynomial expression must have a degree of one (linear factor), and the leading coefficient of the variable in the divisor should be equal to 1. Synthetic division is mainly used to find the zeroes of roots of polynomials. It is used when a polynomial is to be divided by a linear expression and the leading coefficient (first number) must be a 1.

In summary, synthetic division is a simplified method of dividing polynomials with less effort of calculation than the long division method. It is mostly taught for division by linear monic polynomials, but it can be generalized to division by any polynomial. Synthetic division is mainly used to find the zeroes of roots of polynomials when the divisor is a linear factor.