Both processes give the same result, x^2 - 3x - 2. However, synthetic division uses only the coefficients and requires much less writing. To understand synthetic division, we walk you through the process below. Be sure the polynomials are in standard form, that is, each term is arranged in descending order from highest power to lowest.
Step 1: Write the root a determined from (x-a) and the coefficients of the polynomial in the first line.
a by the first coefficient and write the result under the second coefficient.
Here the root (or zero) of (x+5) is -5.
It is interesting to note that the result has a GCF of 2 and we can do the following algebraic manipulations:
Video Lecture: Polynomial Division: Synthetic Division (10 minutes from Mathispower4u)
Divide a Trinomial by a Binomial using Synthetic Division
Divide a Polynomial by a Binomial Using Synthetic Division
Divide Polynomial by a Binomial Using Synthetic Division (with placeholder)