synthetic division


Synthetic divisionMathworldPlanetmath is simply a shorthand for long division, when one of the factors is linear. So when an equation such as

y=2x2+10x+12

is given and a factor of x+3 is known, we can do the following:

2 10 12

First, we can use -3 since -3 is a solution if x+3=0.

-3 2 10 12

Carry down the first coefficientMathworldPlanetmath:

-3 2 10 12
2

Multiply 2 by -3:

-3 2 10 12
-6
2

Add up 10 and -6:

-3 2 10 12
-6
2 4

Multiply 4 by -3:

-3 2 10 12
-6 -12
2 4 0

This means that, by factoring the equation by x+3, we will get another factor as 2x+4.

Synthetic is simply an variation of the long division — a version that’s manipulated and simplified to shorten the calculations.

Title synthetic division
Canonical name SyntheticDivision
Date of creation 2013-03-22 14:07:27
Last modified on 2013-03-22 14:07:27
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 7
Author mathwizard (128)
Entry type Definition
Classification msc 12D05