Polynomial Long Division Calculator
Divide one polynomial by another and follow each subtraction. See the exact quotient and remainder, the reconstruction identity and a substitution check.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide the current leading remainder term by the divisor’s leading term. Add that term to the quotient, multiply the divisor by it and subtract. Repeat until the remainder degree is lower than the divisor degree.
Dividend(x)=Divisor(x)×Quotient(x)+Remainder(x), with deg Remainder < deg Divisor or Remainder=0
Worked example
(x³−2x²−4x+4) ÷ (x−3) gives quotient x²+x−1 and remainder 1. At x=2, the identity reads −4=(−1)×5+1, confirming the calculation.
Assumptions and input details
Each polynomial accepts 1–7 coefficients in descending powers, including zeros for missing powers. Whole numbers, fractions and decimals with up to six places are accepted, within magnitude 1e6 and reduced denominator 1e6. The divisor cannot be the zero polynomial. Constant divisors and dividends of smaller degree are supported. The polynomial identity remains valid at every x, including zeros of the divisor; interpreting the original quotient as a rational function additionally requires Divisor(x)≠0. The verification point follows the same fraction input limits.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Quotient, remainder, long-division steps and the substitution check use exact fraction arithmetic.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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