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first determine our root divisor:
To find our root, we solve the divisor equation
We add 6 to each side of the equation to get
Therefore, our root becomes
Step 1: Write down our coefficients horizontally and our root of 6 to the left:
... | 7 -45 18
6 |_____________________________
Step 2: Bring down the first coefficient of 7
... | 7 -45 18
6 |_____________________________
....... 7
Step 3: Multiply our root of 6 by our last result of 7 to get 42 and put that in column 2:
... | 7 -45 18
6 |......42
_____________________________
....... 7
Step 4: Add the new entry of 42 to our coefficient of -45 to get -3 and put this in the answer column 2:
... | 7 -45 18
6 |......42
_____________________________
....... 7 -3
Step 5: Multiply our root of 6 by our last result of -3 to get -18 and put that in column 3:
... | 7 -45 18
6 |......42 -18
_____________________________
....... 7 -3
Step 6: Add the new entry of -18 to our coefficient of 18 to get 0 and put this in the answer column 3:
Our synthetic division is complete. The values in our results row form a new equation, which has a degree 1 less than our original equation shown below:
Since the last number in our result line is equal to , we will not have a remainder and have a clean quotient which is shown below in our answer:
