Synthetic Division Calculator (Free, Step-by-Step)

Use this free synthetic division calculator to divide a polynomial by a linear factor (x − c). Enter the coefficients and c to get the quotient, the remainder, the complete synthetic-division table, and step-by-step working.

How synthetic division works

List the coefficients (using 0 for any missing power). Bring down the first, multiply by c, add to the next, and repeat. The last number is the remainder; the rest are the quotient’s coefficients. By the Remainder Theorem, that remainder equals P(c).

The Ultimate Algebra Bundle: From Pre-Algebra to Algebra II

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

How to use it

1. Enter the coefficients from highest power to constant.
2. Enter c (to divide by x − c).
3. Press Divide.

Related: the Polynomial Division Calculator and more free math calculators.

Frequently asked questions

What does the remainder tell me?

By the Remainder Theorem it equals P(c). If it is 0, then (x − c) is a factor of the polynomial.

The Ultimate Middle School Math Bundle: Grades 6-8

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

What if a power is missing?

Enter 0 for that coefficient so every power is accounted for.

The Ultimate Elementary School Math Bundle: Grade 3-5

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Can c be negative or a fraction?

Yes — to divide by (x + 3) use c = −3; decimals and fractions are fine.

Pre-Algebra for Beginners 2026: The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.