Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.
2
|
12
-67
108
-47
6
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 12)
2
|
12
-67
108
-47
6
|
12
Multiply 2 by 12 and place the product (which is 24) right underneath the second coefficient (which is -67)
2
|
12
-67
108
-47
6
|
24
12
Add 24 and -67 to get -43. Place the sum right underneath 24.
2
|
12
-67
108
-47
6
|
24
12
-43
Multiply 2 by -43 and place the product (which is -86) right underneath the third coefficient (which is 108)
2
|
12
-67
108
-47
6
|
24
-86
12
-43
Add -86 and 108 to get 22. Place the sum right underneath -86.
2
|
12
-67
108
-47
6
|
24
-86
12
-43
22
Multiply 2 by 22 and place the product (which is 44) right underneath the fourth coefficient (which is -47)
2
|
12
-67
108
-47
6
|
24
-86
44
12
-43
22
Add 44 and -47 to get -3. Place the sum right underneath 44.
2
|
12
-67
108
-47
6
|
24
-86
44
12
-43
22
-3
Multiply 2 by -3 and place the product (which is -6) right underneath the fifth coefficient (which is 6)
2
|
12
-67
108
-47
6
|
24
-86
44
-6
12
-43
22
-3
Add -6 and 6 to get 0. Place the sum right underneath -6.
2
|
12
-67
108
-47
6
|
24
-86
44
-6
12
-43
22
-3
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 (12,-43,22,-3) form the quotient
(