Polynomial division walkthrough
Divide one polynomial by another with exact fractions and see every long or synthetic division step. The result shows the quotient, the remainder and a checked identity.
Each polynomial is limited to 1,000 characters, 512 symbols, 24 nesting levels, degree 64 and 100 digits per number; exact values may grow to 1,024 digits. Everything is computed on your device in a background worker with a 15 second limit. Downloads are a JSON report and a CSV table of steps. One variable, whole-number powers and exact numbers such as 1/2. Up to 1,000 characters. Review the settings before running.
Your result
How to use Polynomial division walkthrough
- Type the dividend polynomial, such as 2x^4 - 3x^3 + 5x - 7.
- Enter the divisor and choose long or synthetic division.
- Run the division and read each step, the quotient and the remainder.
- Download the JSON report or the CSV table of steps.
Useful next steps
How the division works
Each step divides the leading term of the current remainder by the leading term of the divisor, multiplies the divisor by that quotient term and subtracts. Synthetic division does the same work for a divisor x - c using only coefficients. All arithmetic uses exact fractions, so 1/3 stays 1/3. The tool then checks that divisor times quotient plus remainder equals the dividend exactly. Method: OpenStax, College Algebra 2e, section 5.4 Dividing Polynomials (2021).
What you can enter
Use one variable, whole-number powers and numbers such as 3, 0.25 or 1/2. You can write 2x for 2*x and 3(x+1) for 3*(x+1). Functions, other variables and negative powers are rejected with a message instead of being guessed.