✖️Factoring Calculator
Factor any polynomial fully — GCF, difference of squares, trinomials, cubes, and grouping — with step-by-step working and a verification check.
Step-by-step working
Free Factoring Calculator with Steps
Need to factor a polynomial? Our free factoring calculator breaks down any expression fully — greatest common factor, difference of squares, perfect square trinomials, sum and difference of cubes, quadratic trinomials, and grouping — and shows every step labelled by technique, so you understand what's happening at each stage.
Enter your polynomial in standard notation, and the solver works through the strategies in the correct order, applying each one that fits until the expression is fully factored. Fractional and integer coefficients are handled correctly, and if the polynomial is irreducible over the rationals, you'll be told so clearly rather than left with a blank output. A verification step expands the factored form to confirm it matches your original expression.
Simply enter your polynomial to factor it instantly. No sign-up, no downloads, no limits — just clear, step-by-step factoring with the working shown.
About the Factoring Calculator
Features
Ordered strategy detection
GCF is always checked first, then patterns are identified and labelled as each factor is found.
Step-by-step labelled working
Every stage names the technique — GCF, difference of squares, trinomial, and more.
Prime/irreducible detection
Polynomials that can't be factored further over the rationals are clearly labelled, never left blank.
Verification step
The factored result is expanded and checked against your original expression.
Copy result
Copy the fully factored expression as plain text with one click.
Fully client-side
All computation runs in your browser — no data ever leaves your device.
Why factoring matters
Factoring rewrites a polynomial as a product of simpler expressions, which is fundamental to solving equations, simplifying rational expressions, and understanding the roots and behaviour of a function. It's one of the core algebra skills that underpins later work in calculus and applied mathematics.
Frequently Asked Questions
What does this calculator do?
It takes any polynomial expression and factors it fully, showing which technique (GCF, difference of squares, trinomial, etc.) was applied at each step.
Which factoring techniques does it use?
Greatest common factor, difference of squares, perfect square trinomials, sum and difference of cubes, quadratic trinomials, and factoring by grouping — applied in the correct order.
Does it show the working?
Yes. Every factoring step is shown and labelled by technique so you can follow and learn the method, not just copy the result.
What if the polynomial can't be factored?
If the expression is irreducible over the rationals, it says so clearly with a brief explanation rather than returning a blank or wrong answer.
Can it handle higher-degree polynomials?
Yes, as far as it can find rational roots. Simple cases like x^4 - 16 factor via repeated application of the technique.
How do I enter exponents?
Use ^ or ** for powers (e.g. x^2 or x**2), and write coefficients directly before the variable (e.g. 3x^2 - 5x + 2).
Is there a verification step?
Yes. The factored result is expanded and checked against the original to confirm correctness, shown at the end of the working.
Can it factor expressions with two variables?
Single-variable polynomials are the primary and only supported case; a clear message is shown if a second variable is detected.
Is my input sent anywhere?
No. All computation runs entirely in your browser; your expressions never leave your device.
Does it work on mobile?
Yes, fully responsive; the input, working, and factored result display fit any screen without overflow.