What is polynomial long division?
Polynomial long division is a method for dividing one polynomial by another. It works in a similar way to ordinary long division with numbers: divide the leading terms, multiply, subtract, and repeat until the remaining polynomial has a lower degree than the divisor.
How to use this polynomial long division calculator
Enter the dividend and divisor, then select Divide polynomials. The calculator returns the quotient and remainder and shows the main division steps. This makes it useful as a long division polynomials calculator for checking algebra work.
Polynomial division formula
Dividend = (Divisor × Quotient) + Remainder
The remainder must have a lower degree than the divisor.
Example
(x3 + 2x2 - 5x + 6) ÷ (x - 2)
Quotient = x2 + 4x + 3
Remainder = 12
So the result can be written as x2 + 4x + 3 + 12/(x - 2).
Dividing polynomials by long division
For each step, divide the leading term of the current remainder by the leading term of the divisor. Multiply the divisor by that term, subtract it from the current remainder, and continue. When the remainder has a lower degree than the divisor, the process is complete.
Frequently asked questions
Can I use this as a dividing polynomials by long division calculator?
Yes. Enter a polynomial dividend and divisor and the calculator performs the long-division process and reports the quotient and remainder.
What is the difference between polynomial division and long division?
Polynomial long division is a specific algorithm for polynomial division. It repeatedly divides leading terms and subtracts the resulting product.
Can I divide polynomials with missing powers?
Yes. Terms that are not written are treated as having a coefficient of zero.
What happens if the divisor is a constant?
The calculator can divide by a non-zero constant and returns the resulting polynomial.
Does this calculator show the remainder?
Yes. It shows both the quotient and the remainder so you can check the result with the division identity.