Polynomial Division
Divide one polynomial by another using synthetic or long division, showing quotient and remainder.
About Polynomial Division
Polynomial long division works like numeric long division. At each step, divide the leading term of the current dividend by the leading term of the divisor to get the next quotient term, multiply the entire divisor by that term, and subtract from the dividend. Repeat until the remaining degree is less than the divisor's degree.
Formula
Division algorithm
P(x) = Q(x)·D(x) + R(x), deg(R) < deg(D)
- P
- Dividend polynomial
- Q
- Quotient
- D
- Divisor
- R
- Remainder
Worked example
With the default values below, Polynomial Division returns Quotient of 1x^2 - 5x + 6. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Dividend coefficients (highest to lowest)
- 1,-6,11,-6
- Divisor coefficients (highest to lowest)
- 1,-1
Results
- Quotient
- 1x^2 - 5x + 6
- Remainder
- 0
Step by step
- 1Values used
- 2Division algorithm
- 3Quotient= 1x^2 - 5x + 6
- 4Remainder= 0
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How do I enter the polynomials?
Enter coefficients from highest degree to lowest, separated by commas. For x³−6x²+11x−6, enter '1,-6,11,-6'. Include zeros for missing powers.
What is synthetic division?
Synthetic division is a shortcut for dividing by a linear factor (x−c). This calculator uses long division which works for any divisor degree.