📐Polynomial Long Division Calculator
Divide one polynomial by another and see the full step-by-step working.
Use ^ for powers, terms separated by + or −. Example: x^3 - 2x^2 - 4 ÷ x - 3
Free Polynomial Long Division Calculator
This polynomial long division calculator divides one polynomial by another, showing the quotient and remainder along with every intermediate step — just like doing it by hand, but instant. At each step, the calculator divides the leading term of the remaining polynomial by the leading term of the divisor, multiplies that back through, and subtracts.
The result is written as Dividend = Quotient × Divisor + Remainder, which you can verify by expanding back out. Works for any polynomial degree, not just quadratics.
Free, runs entirely in your browser, no sign-up required.
About the Polynomial Long Division Calculator
Features
Any polynomial degree
Works for divisors and dividends of any degree.
Step-by-step
See each subtraction and the new remainder at every step.
Quotient and remainder
Both results displayed clearly.
Instant, private
Runs entirely in your browser. No data is sent anywhere.
Frequently Asked Questions
How does polynomial long division work?
Divide the leading term of the dividend by the leading term of the divisor to get the next quotient term, multiply that term by the whole divisor, subtract it from the dividend, and repeat with the new remainder until its degree is lower than the divisor's.
What does 'quotient' and 'remainder' mean here?
The quotient is the polynomial result of the division; the remainder is what's left over that couldn't be divided further, with degree lower than the divisor.
How do I check my answer?
Verify that Dividend = Quotient × Divisor + Remainder. Expanding the right side should give back exactly the original dividend.
What if the remainder is zero?
A zero remainder means the divisor divides the dividend evenly — the divisor is a factor of the dividend.
What input format is expected?
Standard polynomial notation using ^ for exponents and + or − between terms, like x^3 - 2x^2 - 4.
Can the divisor have a higher degree than the dividend?
Yes — in that case the quotient is simply 0 and the remainder equals the original dividend, since no division steps can occur.
Is this the same as synthetic division?
Synthetic division is a shortcut specifically for dividing by a linear factor (x − c). Long division works for divisors of any degree and shows more of the underlying process.
Why divide polynomials at all?
It's used to factor higher-degree polynomials, find roots, simplify rational expressions, and perform partial fraction decomposition.
Does it work with fractional or negative coefficients?
Yes, coefficients can be any real number, positive or negative, including decimals.
Is this calculator free to use?
Yes, completely free with no sign-up, and it runs entirely in your browser.