Polynomial Division Calculator
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Polynomial Division Methods
Long Division
Similar to numerical long division:
- Divide the highest degree term of the dividend by the highest degree term of the divisor
- Multiply the divisor by the result
- Subtract from the dividend
- Repeat until the degree of the remainder is less than the divisor
Synthetic Division
A shortcut method for dividing by linear factors:
- Write the coefficients of the dividend
- Use the root of the divisor (x - r)
- Bring down the first coefficient
- Multiply and add until complete
Example Problems
Example 1: Long Division
Divide: (x³ + 2x² - 5x - 6) ÷ (x + 2)
Step 1: Set up the division
x + 2 | x³ + 2x² - 5x - 6
Step 2: Perform division
Result: x² - 5x + 5 with remainder -16
Example 2: Synthetic Division
Divide: (x³ - 4x² + 5x - 2) ÷ (x - 2)
Step 1: Set up synthetic division
Step 2: Use root x = 2
Result: x² - 2x + 1 with remainder 0
When to Use Each Method
| Method | Best For |
|---|---|
| Long Division | Any polynomial division, especially when divisor is not linear |
| Synthetic Division | Dividing by linear factors (x - r), faster than long division |
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