Now set up the synthetic division table by placing the test zero in the upperleft corner and placing the coefficients of the numerator to the right of the test zero.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like
-1
|
2
0
-8
0
6
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)
-1
|
2
0
-8
0
6
2
Multiply -1 by 2 and place the product (which is -2) right underneath 0
-1
|
2
0
-8
0
6
-2
2
Add -2 and 0 to get -2. Place the sum right underneath -2.
-1
|
2
0
-8
0
6
-2
2
-2
Multiply -1 by -2 and place the product (which is 2) right underneath -8
-1
|
2
0
-8
0
6
-2
2
2
-2
Add 2 and -8 to get -6. Place the sum right underneath 2.
-1
|
2
0
-8
0
6
-2
2
2
-2
-6
Multiply -1 by -6 and place the product (which is 6) right underneath 0
-1
|
2
0
-8
0
6
-2
2
6
2
-2
-6
Add 6 and 0 to get 6. Place the sum right underneath 6.
-1
|
2
0
-8
0
6
-2
2
6
2
-2
-6
6
Multiply -1 by 6 and place the product (which is -6) right underneath 6
-1
|
2
0
-8
0
6
-2
2
6
-6
2
-2
-6
6
Add -6 and 6 to get 0. Place the sum right underneath -6.
-1
|
2
0
-8
0
6
-2
2
6
-6
2
-2
-6
6
0
Since the last column adds to zero, we have a remainder of zero. This means is a factor of
Now lets look at the bottom row of coefficients:
The first 4 coefficients (2,-2,-6,6) form the quotient
Notice in the denominator , the x term has a coefficient of 2, so we need to divide the quotient by 2 like this:
(