Synthetic Division Calculator
Divide any polynomial by a divisor like (x - 1) in seconds: enter the root and the coefficients, and get the step-by-step synthetic division table with the quotient and remainder.
How to use
- If the divisor is in the form (x - c), enter c. (x + 2) means c = -2.
- Enter the coefficients for each power, separated by commas — write 0 for any missing power.
- The table below shows the bring-down, multiply and add steps; the last number is the remainder.
Note: Remainder theorem: the remainder is the same as putting x = c into the polynomial, P(c). If the remainder is zero, (x - c) is a factor (factor theorem).
Frequently Asked Questions (FAQ)
What inputs does the synthetic division calculator need?
The divisor root c for (x - c), and the polynomial coefficients from the highest power down to the constant, with 0 for missing powers.
What does the result show?
The step-by-step bring-down, multiply and add table, the quotient and the remainder.
How is the remainder related to the remainder theorem?
The remainder equals P(c), the polynomial evaluated at the root. If it is zero, (x - c) is a factor.
What value do I enter for a divisor like (x + 2)?
Enter c = -2. Synthetic division needs the divisor in the form (x - c), so (x + 2) means c is -2.