Math Solver / Factoring Calculator

Factoring Calculator

Factor polynomials, trinomials and special products — with the expanded form shown alongside.

Press Enter to solve · ^ for powers · sqrt() for roots · separate a system with a comma

Try:

The factoring calculator rewrites a polynomial as a product of simpler factors. Enter x^2 + 5x + 6, 2x^2 - 8 or x^3 - 8 and you get the factored form, the method hint and the expanded form for comparison.

How to use the factoring calculator

  1. Type the polynomial without an equals sign.
  2. Keep the Factor tab selected (or type “factor” first).
  3. Press Enter.

Factoring methods

Greatest common factor

Take out what every term shares: 6x² + 9x = 3x(2x + 3).

Trinomials x² + bx + c

Find two numbers that multiply to c and add to b: x² + 5x + 6 = (x + 2)(x + 3).

Difference of squares

a² − b² = (a − b)(a + b), so x² − 9 = (x − 3)(x + 3).

Sum and difference of cubes

a³ − b³ = (a − b)(a² + ab + b²), so x³ − 8 = (x − 2)(x² + 2x + 4).

Questions about factoring

Why factor a polynomial?

Factored form shows the roots directly: if (x + 2)(x + 3) = 0, then x = −2 or x = −3. It also simplifies fractions with polynomials.

What if a polynomial cannot be factored?

Some polynomials, such as x² + x + 1, do not factor over the integers. Use the quadratic solver to find their roots instead.

Can I expand instead?

Yes. Choose the Expand tab or type expand (x + 3)(x - 2).

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