Rational Root Theorem
where p and q are factors to the last and first coefficients
So lets list the factors of 8
Now let's list the factors of 1
Now lets divide them
Now simplify
So these are possible zeros. To find out which possible zero is actually a zero, you need to perform synthetic division on each one.
Lets test -2 as a zero
So our test zero is -2
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
|
1
6
12
8
|
Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
-2
|
1
6
12
8
|
1
Multiply -2 by 1 and place the product (which is -2) right underneath the second coefficient (which is 6)
-2
|
1
6
12
8
|
-2
1
Add -2 and 6 to get 4. Place the sum right underneath -2.
-2
|
1
6
12
8
|
-2
1
4
Multiply -2 by 4 and place the product (which is -8) right underneath the third coefficient (which is 12)
-2
|
1
6
12
8
|
-2
-8
1
4
Add -8 and 12 to get 4. Place the sum right underneath -8.
-2
|
1
6
12
8
|
-2
-8
1
4
4
Multiply -2 by 4 and place the product (which is -8) right underneath the fourth coefficient (which is 8)
-2
|
1
6
12
8
|
-2
-8
-8
1
4
4
Add -8 and 8 to get 0. Place the sum right underneath -8.
-2
|
1
6
12
8
|
-2
-8
-8
1
4
4
0
Since the last column adds to zero, we have a remainder of zero.
So is a zero. This means is a factor of
Now lets look at the bottom row of coefficients:
The first 3 coefficients (1,4,4) form the quotient
(