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.
4
|
3
-19
27
4
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 3)
4
|
3
-19
27
4
|
3
Multiply 4 by 3 and place the product (which is 12) right underneath the second coefficient (which is -19)
4
|
3
-19
27
4
|
12
3
Add 12 and -19 to get -7. Place the sum right underneath 12.
4
|
3
-19
27
4
|
12
3
-7
Multiply 4 by -7 and place the product (which is -28) right underneath the third coefficient (which is 27)
4
|
3
-19
27
4
|
12
-28
3
-7
Add -28 and 27 to get -1. Place the sum right underneath -28.
4
|
3
-19
27
4
|
12
-28
3
-7
-1
Multiply 4 by -1 and place the product (which is -4) right underneath the fourth coefficient (which is 4)
4
|
3
-19
27
4
|
12
-28
-4
3
-7
-1
Add -4 and 4 to get 0. Place the sum right underneath -4.
4
|
3
-19
27
4
|
12
-28
-4
3
-7
-1
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 3 coefficients (3,-7,-1) form the quotient
(