Synthetic Division Calculator

Multiply our root -3 by 2Take -6 and put that in column 2: Multiply our root -3 by -10Take 30 and put that in column 3: Multiply our root -3 by 8Take -24 and put that in column 4: Leading Answer Term = x(3 - 1) = x2

Synthetic Division Calculator MathCelebrity logo Image to Crop Use synthetic division for:
2x3 - 4x2 - 22x + 24
x + 3

Determine our root divisor:

Solve the divisor equation x + 3 = 0
Subtract 3 from each side of the equation to get
x + 3 - 3 = 0 - 3
Therefore, our root becomes x = -3
                  2         -4         -22         24
  -3                                      
         
                  2         -4         -22         24
  -3           ↓                           
                  2                           

Multiply our root -3 by 2
Take -6 and put that in column 2:

                  2         -4         -22         24
  -3                    -6                  
                  2                           
-6 + -4 = -10
Put this in the answer column 2:
                  2         -4         -22         24
  -3                    -6                  
                  2         -10                  

Multiply our root -3 by -10
Take 30 and put that in column 3:

                  2         -4         -22         24
  -3                    -6         30         
                  2         -10                  
30 + -22 = 8
Put this in the answer column 3:
                  2         -4         -22         24
  -3                    -6         30         
                  2         -10         8         

Multiply our root -3 by 8
Take -24 and put that in column 4:

                  2         -4         -22         24
  -3                    -6         30         -24
                  2         -10         8         
-24 + 24 = 0
Put this in the answer column 4:
                  2         -4         -22         24
  -3                    -6         30         -24
                  2         -10         8         0

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

Since the last number in our result line = 0, we will not have a remainder and have a clean quotient which is shown below in our answer:

Answer  =  2x2 - 10x + 8

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It appears your answer forms a quadratic equation since the maximum power of your result equation is 2 and your remainder is zero. Click here to solve this quadratic equation

How does the Synthetic Division Calculator work?

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem
This calculator has 1 input.

What 3 formulas are used for the Synthetic Division Calculator?

For x + a, our root is -1 * a
Write down our coefficients horizontally and our root of a to the left
Multiply root by last result and repeat process

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Synthetic Division Calculator?

divisionseparate a number into partspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).ruffinis rulean efficient method of dividing a polynomial by a linear factor, with or without a remainder. synthetic divisiona shorthand method for dividing a polynomial by a linear factor

Synthetic Division Calculator Video


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