Synthetic Division Calculator

Enter your numerator coefficients below in the corresponding boxes or
x6 x5 x4 x3 x2 x Constant

<-- Select x + or x - and Enter Root (r) <-- This is your denominator

Using synthetic division (Ruffini's Rule), perform the following division:

 6x3 + x2 - 3 x - 7

Determine our root divisor:
To find our root, we solve the divisor equation x - 7 = 0
We add 7 to each side of the equation to get x - 7 + 7 = 0 + 7
Therefore, our root becomes x = 7

Step 1:  Write down our coefficients horizontally and our root of 7 to the left:

 6 1 0 -3 7

Step 2:  Bring down the first coefficient of 6

 6 1 0 -3 7 ↓ 6

Step 3:  Multiply our root of 7 by our last result of 6 to get 42 and put that in column 2:

 6 1 0 -3 7 42 6

Step 4:  Add the new entry of 42 to our coefficient of 1 to get 43 and put this in the answer column 2:

 6 1 0 -3 7 42 6 43

Step 5:  Multiply our root of 7 by our last result of 43 to get 301 and put that in column 3:

 6 1 0 -3 7 42 301 6 43

Step 6:  Add the new entry of 301 to our coefficient of 0 to get 301 and put this in the answer column 3:

 6 1 0 -3 7 42 301 6 43 301

Step 7:  Multiply our root of 7 by our last result of 301 to get 2107 and put that in column 4:

 6 1 0 -3 7 42 301 2107 6 43 301

Step 8:  Add the new entry of 2107 to our coefficient of -3 to get 2104 and put this in the answer column 4:

 6 1 0 -3 7 42 301 2107 6 43 301 2104

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: