What this calculator does
Synthetic division works out divides a polynomial by (x − r) and returns the quotient and remainder. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaBring down the leading coefficient; each next value = previous result × r + next coefficient; the last value is the remainder
The inputs explained
| Field | What to enter |
|---|---|
| Coefficients, highest degree first | A list of numbers, separated by commas or spaces. |
| Divide by (x − r): value of r | A number. Starts at 1. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with divide by (x − r): value of r
Every other input is held at the calculator’s starting values while divide by (x − r): value of r varies. Select any row to load that scenario into the calculator.
How the answer changes with divide by (x − r): value of r