📐 Synthetic Division Calculator
Divide polynomials by (x - c)
Enter coefficients separated by commas. For x³ + 4x² + x + 6, enter: 1,4,1,6
How to Use This Calculator
Enter Coefficients
Type coefficients in descending order, e.g., 1,4,1,6 for x³ + 4x² + x + 6
Enter Divisor
Type the value of c where you're dividing by (x - c)
Calculate
See the quotient, remainder, and synthetic division process
Synthetic Division Method
Quick method to divide polynomials by (x - c)
Example: Divide x³ + 4x² + x + 6 by (x + 3)
-3 | 1 4 1 6
| -3 -3 6
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1 1 -2 0
Result: x² + x - 2 with remainder 0
About Synthetic Division Calculator
The Synthetic Division Calculator divides polynomials by (x - c) using synthetic division, a faster method than long division. If the remainder is zero, then (x - c) is a factor of the polynomial.
When to Use This Calculator
- Factor Finding: Check if (x - c) is a factor
- Quick Division: Faster than polynomial long division
- Root Testing: Test potential roots quickly
Key Points
- Works only for divisors of form (x - c)
- If remainder is 0, (x - c) is a factor
- Much faster than long division
- Organized in a compact table
Frequently Asked Questions
What if the remainder is zero?
If remainder is 0, then (x - c) is a factor! The polynomial can be factored further.
Can I use synthetic division for other divisors?
Synthetic division only works for divisors of the form (x - c). For other forms, use polynomial long division.