Polynomial Long Division Calculator

This polynomial long division calculator divides one polynomial by another and returns the quotient and the remainder. Enter the coefficients of the dividend and the divisor, highest power first and separated by commas, and the calculator carries out the long division for you. Just like dividing whole numbers, you get a quotient polynomial and a remainder whose degree is lower than the divisor. Polynomial division is used to factorise, to simplify rational expressions, and to apply the factor and remainder theorems. The method, a worked example and the assumptions are below.

Dividend coefficients (high to low)

Divisor coefficients (high to low)

Remainder

Divisor degree

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

Related calculators

Quadratic Formula Calculator: solve a quadratic.
Scientific Calculator: general maths.
Matrix Calculator: matrix operations.

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