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

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.

Free · No sign-up · Runs in your browserLast updated: 2026-10-26

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How to use Polynomial Calculator

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

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.