Polynomial Division
Divide one polynomial by another using synthetic or long division, showing quotient and remainder.
Inputs
e.g. '1,-6,11,-6' for x³−6x²+11x−6
e.g. '1,-1' for x−1
Quotient
1x^2 - 5x + 6
Remainder
0
Step by step
Values used
Dividend coefficients (highest to lowest) = 1,-6,11,-6; Divisor coefficients (highest to lowest) = 1,-1
Division algorithm
P(x) = Q(x)·D(x) + R(x), deg(R) < deg(D)
Quotient
= 1x^2 - 5x + 6
Remainder
= 0
How it works
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
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.