Polynomial Division Calculator — Long & Synthetic (Free)

Use this free polynomial division calculator to divide one polynomial by another. Enter the coefficients of the dividend and divisor and you’ll get the quotient and remainder, the check that dividend = divisor × quotient + remainder, and the full long-division working.

How to use the calculator

1. Enter the dividend’s coefficients (highest power first), e.g. 1, -2, -4 for x² − 2x − 4.
2. Enter the divisor’s coefficients, e.g. 1, -3 for x − 3.
3. Press Calculate to see the quotient, remainder and steps.

Long and synthetic division

The tool performs polynomial long division — divide, multiply, subtract, bring down, repeat — and, when the divisor is linear like (x − r), it also shows the quicker synthetic division row.

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Frequently asked questions

How do you write the coefficients?

List them from the highest power to the constant, including zeros for any missing terms — for x³ − 1 enter 1, 0, 0, −1.

What is the remainder?

What’s left over when the divisor no longer fits. The result always satisfies dividend = divisor × quotient + remainder.

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When can I use synthetic division?

When the divisor is linear, such as x − 3. The calculator shows the synthetic row in that case.

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Read the full lesson: learn the method step by step.

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