Polynomial Division Calculator

Polynomial Division Calculator

Divide one polynomial by another using long division and review the quotient and remainder side by side.

Last updated: March 2026 | By ForgeCalc Engineering

Polynomial Division Solver

Long division

Result Breakdown

Quotient: x + 2
Remainder: 0
Quotient
x + 2
Remainder
0

What Polynomial Division Means

Polynomial division splits a polynomial into a quotient and a remainder. It works like numeric long division, but with terms and powers.

How to Divide Polynomials

  1. Divide the leading term of the dividend by the leading term of the divisor.
  2. Multiply the divisor by that term and subtract.
  3. Repeat until the remainder degree is lower than the divisor degree.
  4. Read the quotient and remainder.
P(x) = D(x)Q(x) + R(x)

Worked Example

Example: Dividing x^2 - 4 by x - 2 gives a quotient of x + 2.

x^2 - 4 = (x - 2)(x + 2)

Frequently Asked Questions

What if the divisor is zero?

Division by zero is not allowed, so the divisor must have a non-zero leading coefficient.

Does this accept decimals?

Yes. Any finite coefficient values are accepted.

What if the remainder is zero?

Then the dividend is divisible by the divisor with no remainder.

Why use coefficient lists?

Coefficient lists make long division easier to compute programmatically.

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