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
|
4
5
-13
-7
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 4)
2
|
4
5
-13
-7
|
4
Multiply 2 by 4 and place the product (which is 8) right underneath the second coefficient (which is 5)
2
|
4
5
-13
-7
|
8
4
Add 8 and 5 to get 13. Place the sum right underneath 8.
2
|
4
5
-13
-7
|
8
4
13
Multiply 2 by 13 and place the product (which is 26) right underneath the third coefficient (which is -13)
2
|
4
5
-13
-7
|
8
26
4
13
Add 26 and -13 to get 13. Place the sum right underneath 26.
2
|
4
5
-13
-7
|
8
26
4
13
13
Multiply 2 by 13 and place the product (which is 26) right underneath the fourth coefficient (which is -7)
2
|
4
5
-13
-7
|
8
26
26
4
13
13
Add 26 and -7 to get 19. Place the sum right underneath 26.
2
|
4
5
-13
-7
|
8
26
26
4
13
13
19
Since the last column adds to 19, we have a remainder of 19. This means is not a factor of
Now lets look at the bottom row of coefficients:
The first 3 coefficients (4,13,13) form the quotient
and the last coefficient 19, is the remainder.
So the remainder is 19
note: it looks like you added -26 and -7 to get -33. Instead you should add 26 and -7 to get 19
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