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.
-3
|
1
5
-6
10
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
-3
|
1
5
-6
10
|
1
Multiply -3 by 1 and place the product (which is -3) right underneath the second coefficient (which is 5)
-3
|
1
5
-6
10
|
-3
1
Add -3 and 5 to get 2. Place the sum right underneath -3.
-3
|
1
5
-6
10
|
-3
1
2
Multiply -3 by 2 and place the product (which is -6) right underneath the third coefficient (which is -6)
-3
|
1
5
-6
10
|
-3
-6
1
2
Add -6 and -6 to get -12. Place the sum right underneath -6.
-3
|
1
5
-6
10
|
-3
-6
1
2
-12
Multiply -3 by -12 and place the product (which is 36) right underneath the fourth coefficient (which is 10)
-3
|
1
5
-6
10
|
-3
-6
36
1
2
-12
Add 36 and 10 to get 46. Place the sum right underneath 36.
-3
|
1
5
-6
10
|
-3
-6
36
1
2
-12
46
Since the last column adds to 46, we have a remainder of 46. This means is not a factor of
Now lets look at the bottom row of coefficients:
The first 3 coefficients (1,2,-12) 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
(