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
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
- Type the polynomial without an equals sign.
- Keep the Factor tab selected (or type “factor” first).
- 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).