| 3x4 + 6x3 - 123x2 - 126x + 1080 |
| x + 4 |
Determine our root divisor:
Solve the divisor equation x + 4 = 0Subtract 4 from each side of the equation to get
x + 4 - 4 = 0 - 4
Therefore, our root becomes x = -4
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | |||||
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | ↓ | ||||
| 3 |
Multiply our root -4 by 3
Take -12 and put that in column 2:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | ||||
| 3 |
Put this in the answer column 2:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | ||||
| 3 | -6 |
Multiply our root -4 by -6
Take 24 and put that in column 3:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | |||
| 3 | -6 |
Put this in the answer column 3:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | |||
| 3 | -6 | -99 |
Multiply our root -4 by -99
Take 396 and put that in column 4:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | 396 | ||
| 3 | -6 | -99 |
Put this in the answer column 4:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | 396 | ||
| 3 | -6 | -99 | 270 |
Multiply our root -4 by 270
Take -1080 and put that in column 5:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | 396 | -1080 | |
| 3 | -6 | -99 | 270 |
Put this in the answer column 5:
| 3 | 6 | -123 | -126 | 1080 | |
| -4 | -12 | 24 | 396 | -1080 | |
| 3 | -6 | -99 | 270 | 0 |
Leading Answer Term = x(4 - 1) = x3
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 = 3x3 - 6x2 - 99x + 270
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It appears your answer forms a cubic equation since the maximum power of your result equation is 3 and your remainder is zero. Click here to solve this cubic 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 * aWrite 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?
- division
- separate a number into parts
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- ruffinis rule
- an efficient method of dividing a polynomial by a linear factor, with or without a remainder.
- synthetic division
- a shorthand method for dividing a polynomial by a linear factor
