Factoring Calculator

Factor any polynomial — common factors, trinomials, difference of squares, grouping — with the reasoning shown.

Try an example:

What factoring means

Factoring rewrites an expression as a product of simpler expressions. It's the reverse of expanding: $(x + 3) (x + 4)$ expands to $x^{2} + 7 x + 12$ , so factoring $x^{2} + 7 x + 12$ gives $(x + 3) (x + 4)$ .

Factored form is useful because a product is zero only when one of its factors is zero — which is how many equations get solved.

How to use the factoring calculator

Type or paste your problem into the box above — for example x^2 + 7x + 12. Use ^ for powers, / for fractions and sqrt() for square roots, or describe it in words.
Press Enter. The solver works through the problem with every step shown; switch Steps off if you only want the final answer.
Ask a follow-up in the same chat — "why did you do that?" or "now check it" — and it answers with the earlier working in context.

Patterns to recognise

Greatest common factor: $6 x^{3} + 9 x^{2} = 3 x^{2} (2 x + 3)$
Difference of squares: $a^{2} - b^{2} = (a - b) (a + b)$
Perfect square trinomial: $a^{2} + 2 ab + b^{2} = (a + b)^{2}$
Sum and difference of cubes: $a^{3} \pm b^{3} = (a \pm b) (a^{2} \mp ab + b^{2})$

A reliable order to try

Always take out the greatest common factor first.
Count the terms. Two suggest a difference of squares or cubes, three suggest a trinomial, and four suggest grouping.
For $a x^{2} + b x + c$ , find two numbers that multiply to $a c$ and add to $b$ , split the middle term and factor by grouping. Expand your answer to check it.

Worked example: $6 x^{2} + 11 x - 10$

Find $a c$ $a = 6$ and $c = - 10$ , so $a c = - 60$ .
Find the pairTwo numbers that multiply to $- 60$ and add to $11$ : $15$ and $- 4$ .
Split the middle term $6 x^{2} + 15 x - 4 x - 10$
Factor by grouping $3 x (2 x + 5) - 2 (2 x + 5) = (3 x - 2) (2 x + 5)$
Check by expanding $(3 x - 2) (2 x + 5) = 6 x^{2} + 15 x - 4 x - 10 = 6 x^{2} + 11 x - 10$

Common mistakes to avoid

Stopping too early

$2 x^{2} - 8 = 2 (x^{2} - 4)$ isn't finished — $x^{2} - 4$ factors again, into $(x - 2) (x + 2)$ .

Treating a sum of squares like a difference

$x^{2} + 9$ doesn't factor over the real numbers. Only $a^{2} - b^{2}$ splits into $(a - b) (a + b)$ .

Sign errors in grouping

When the second group starts with a minus, factor out the negative: $- 4 x - 10 = - 2 (2 x + 5)$ .

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Questions students ask

Can it factor cubics and higher-degree polynomials?

Yes. It looks for common factors, special patterns and rational roots, and explains which one works.

What if an expression can't be factored?

The solver says so and explains why. For example, a quadratic whose discriminant isn't a perfect square has no factors with integer coefficients.

Can it factor expressions with two variables?

Yes, such as $x^{2} - 5 x y + 6 y^{2} = (x - 2 y) (x - 3 y)$ .

How do I type exponents?

Use the caret: type x^3 for $x^{3}$ .