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:
Leading Answer Term = x(3 - 1) = x2

Since the last number in our result line of 2104 does not equal 0, our answer will have a remainder. We take this term and divide it by our (x - r) root which is x - 7 shown below in our answer:

Answer  =
 
6x2 + 43x + 301 +
 
2104
x - 7