# Polynomial Calculator - Roots, Factoring, Arithmetic and Long Division

> Free online polynomial calculator: type x^3-2x^2-5x+6 for all real and complex roots, factoring, the derivative and antiderivative, plus long division.

- URL: https://qilingtools.com/en/math/polynomial
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Type the polynomial the way you would write it. You get every real and complex root (Durand–Kerner iteration), exact rational roots, factoring by the real roots, the derivative, the antiderivative and the value at any point — plus addition, subtraction, multiplication and long division with a remainder.

## How to use

1. Choose roots and values, arithmetic, or division
2. Enter the polynomial, e.g. x^3-2x^2-5x+6 (and a divisor for division)
3. Read the results and copy the standard form or any value

## Features

- Durand–Kerner iteration finds all complex roots, with the real ones filtered out
- Exact rational roots for integer coefficients (such as 1/2 or -3)
- Factoring by the real roots, with the sum and product of the roots
- Derivative, antiderivative and the value at a chosen point
- Addition, subtraction, multiplication and long division with a verification line

## FAQ

### How do I type a polynomial?

Just as in a textbook: x^3-2x^2-5x+6, 2x^2+3, -x^5+x. The multiplication sign can be omitted, coefficients may be decimal or negative, and the degree can go up to 12.

### How are the roots found?

The Durand–Kerner iteration converges to all complex roots at once; roots with a near-zero imaginary part are reported as real. For integer coefficients the rational root theorem also gives exact values.

### Why does the factoring end with an ellipsis?

Because some roots are complex. Over the reals you can only split off linear factors for the real roots; the remaining quadratic factor has no real roots.

### What is the remainder in polynomial division?

What is left after long division, with a degree lower than the divisor. The tool shows the quotient and remainder and verifies divisor × quotient + remainder against the original.

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