What polynomials can this tool factor?

It supports degree-2 (quadratic, ax²+bx+c) and degree-3 (cubic, ax³+bx²+cx+d) polynomials with real numeric coefficients.

What if the polynomial has complex roots?

Complex roots are displayed in a+bi form. The factored expression uses these complex factors so the result is always complete and mathematically correct.

What does a leading coefficient of zero mean?

If a = 0, the degree is reduced by one. The tool will alert you to use the lower-degree mode instead.

How accurate are the roots?

Roots are computed using double-precision floating-point arithmetic and displayed to 6 significant figures. For exact fractions, verify by hand if needed.

Does the tool show steps?

Yes. The discriminant (for quadratics) or the depressed cubic parameters are shown alongside the roots and factored form.

Polynomial Factoring Calculator

Enter the coefficients of a quadratic or cubic polynomial and instantly get its factored form and all roots.

Polynomial Coefficients

Polynomial Degree

a (x²)

b (x)

c (const)

d (const)

Enter coefficients and click Factor Polynomial to see results.

Summary

This polynomial factoring calculator factors quadratic and cubic polynomials into their root-based factored form. Enter the coefficients and the tool computes real roots using the quadratic formula or Cardano's method, then displays the full factored expression. Complex (non-real) roots are shown in a+bi notation so no information is lost.

How it works

Select the degree of your polynomial: quadratic (degree 2) or cubic (degree 3).
Enter each coefficient (a, b, c, and optionally d) into the input fields.
Click "Factor" or let the tool compute on input change.
The calculator finds all roots using the quadratic formula or Cardano's method.
The factored form and each root are displayed with full step-by-step detail.

Use cases

Factor a quadratic equation for algebra homework.
Find all roots of a cubic polynomial in engineering problems.
Verify hand-factored results against a reliable calculator.
Understand whether a polynomial has real or complex roots.
Decompose polynomials before applying partial fractions.
Quickly check discriminant sign for solution classification.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu