Polynomial Synthetic Division
Polynomial Synthetic Division: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Divisor must be monic and linear: x−r.
Example Calculation
- Dividend coefficients: 1, -3, 2
- r in divisor x−r: 1
(x²−3x+2)/(x−1) = x−2 with remainder 0.
Method references
Frequently asked questions
How do I use this calculator?
Enter dividend coefficients, r in divisor x−r. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Bring down the leading coefficient; repeatedly multiply by r and add. The final value is the remainder.. Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Divisor must be monic and linear: x−r.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.