Polynomial Long Division Calculator
This calculator divides one polynomial by another using long division and returns the quotient and the remainder, the same result you would get working through the division by hand. Enter the coefficients of the dividend and the divisor as comma-separated numbers, listed from the highest power down to the constant term, using 0 to hold the place of any power that does not appear. As you type, the calculator divides the leading terms and subtracts repeatedly, the same steps you would follow by hand, and updates the result automatically. It returns three things: the quotient as the main result, the remainder, and the divisor degree, so you can see how far the division has been carried and whether it divides exactly. A remainder of zero tells you the divisor is a factor of the dividend, which is useful for factorising expressions, simplifying rational functions, and applying the factor and remainder theorems. You can check any answer by confirming that dividend equals divisor times quotient plus remainder, and the worked example on this page shows that check in action. Coefficients can be positive, negative or fractional, and results are rounded to six decimal places for display, so small rounding differences may appear with non-integer inputs. It is a quick, reliable tool for algebra students, tutors and anyone working through polynomial division who wants to check their working.
The formula
Dividing polynomial P by D gives a quotient Q and remainder R with P = D times Q + R, where the degree of R is less than the degree of D. The calculator divides leading terms repeatedly, subtracting each time.
Worked example
Dividing x^2 minus 1 by x minus 1 gives quotient x + 1 (coefficients 1, 1) and remainder 0, since x^2 minus 1 = (x minus 1)(x + 1). Enter 1, 0, -1 and 1, -1 to confirm.
Frequently asked questions
How do I enter a polynomial?
List the coefficients from the highest power down to the constant, separated by commas. Use 0 for any missing power.
What is the remainder?
What is left over after dividing, with a degree lower than the divisor. A remainder of 0 means the divisor is a factor.
How is this checked?
Dividend equals divisor times quotient plus remainder. The pieces should rebuild the original.
Who this calculator is for
This calculator is for algebra students and anyone needing a quick, reliable result.
What this calculator assumes
- You enter valid numbers.
- The standard method is applied.
- Results are rounded for display.
Formula and sources
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