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. This is simply because really looks like
-3
|
2
0
-10
6
-8
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2)
-3
|
2
0
-10
6
-8
2
Multiply -3 by 2 and place the product (which is -6) right underneath 0
-3
|
2
0
-10
6
-8
-6
2
Add -6 and 0 to get -6. Place the sum right underneath -6.
-3
|
2
0
-10
6
-8
-6
2
-6
Multiply -3 by -6 and place the product (which is 18) right underneath -10
-3
|
2
0
-10
6
-8
-6
18
2
-6
Add 18 and -10 to get 8. Place the sum right underneath 18.
-3
|
2
0
-10
6
-8
-6
18
2
-6
8
Multiply -3 by 8 and place the product (which is -24) right underneath 6
-3
|
2
0
-10
6
-8
-6
18
-24
2
-6
8
Add -24 and 6 to get -18. Place the sum right underneath -24.
-3
|
2
0
-10
6
-8
-6
18
-24
2
-6
8
-18
Multiply -3 by -18 and place the product (which is 54) right underneath -8
-3
|
2
0
-10
6
-8
-6
18
-24
54
2
-6
8
-18
Add 54 and -8 to get 46. Place the sum right underneath 54.
-3
|
2
0
-10
6
-8
-6
18
-24
54
2
-6
8
-18
46
Since the last column adds to 46, we have a remainder of 46. This means is a not factor of
Now lets look at the bottom row of coefficients:
The first 4 coefficients (2,-6,8,-18) form the quotient
and the last coefficient 46, is the remainder, which is placed over like this
Putting this altogether, we get:
So
which looks like this in remainder form:
remainder 46
(