In algebra, synthetic division is one of the methods used to manually perform the Euclidean division of polynomials. The division of polynomials can also be done using the long division method. Understand the synthetic division step-wise method using solved examples.
In this lesson, I’ll walk you through five examples that should help you get comfortable with the basic steps needed to divide polynomials using synthetic division.
Below is a step-by-step solution for the division of any linear polynomial with the help of the synthetic division method. Let’s walk through the synthetic division of dividing: 4x2 - 6x -8 by x - 2 step-by-step.
A step-by-step guide to doing synthetic division on any polynomial Synthetic division is a shorthand method of dividing polynomials where you divide the coefficients of the polynomials, removing the variables and exponents. It allows you...
Synthetic division is a shorthand method for dividing a polynomial by a linear factor such as x + 3, and it's much simpler and faster.
I only know how to use synthetic division with a linear coefficient equal to 1, but I'm told that there is a way to do this kind of division, too. As we’ve seen, synthetic division applies directly only when the divisor has the form \ ( (x-c)); but it can be extended easily.
In the synthetic division method, we will perform multiplication and addition, in the place of division and subtraction, which is used in the long division method.
And remember, the type of synthetic division we're doing, it only applies when we are dividing by an x plus or minus something. There's a slightly different process you would have to do if it was 3x or if was negative 1x or if it was 5x squared.