Synthetic Division Calculator
x³ +
x² +
x +
x -
Result
Synthetic Division
Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form (x - k).
Steps:
- Write the coefficients of the polynomial in descending order
- Write k (from x - k) to the left
- Bring down the first coefficient
- Multiply by k and add to the next coefficient
- Repeat until all coefficients are used
- The last number is the remainder
Example Problems
Example 1:
Divide x³ + 2x² - 5x - 6 by (x - 2)
Solution Steps:
- Write coefficients: 1, 2, -5, -6
- k = 2
- Synthetic division table:
| 2 | 1 | 2 | -5 | -6 |
| 2 | 8 | 6 | ||
| 1 | 4 | 3 | 0 |
Result: x² + 4x + 3 with remainder 0
Example 2:
Divide x³ - 3x² + 4x - 12 by (x - 3)
Solution Steps:
- Write coefficients: 1, -3, 4, -12
- k = 3
- Synthetic division table:
| 3 | 1 | -3 | 4 | -12 |
| 3 | 0 | 12 | ||
| 1 | 0 | 4 | 0 |
Result: x² + 4 with remainder 0
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