Factoring Calculator

Tip: drag a photo here or paste a screenshot (Ctrl+V)

How are solve allowances used?

Math, physics, chemistry and all AI tools share your plan allowance.

Each successful standard AI submission uses one standard solve. Deep reasoning uses one deep solve instead. Both count toward the daily solve limit.

Photos and selected PDF pages also use one daily photo solve per submission. Uploading a file or selecting a page does not start a solve. PDF upload requires Plus or Pro.

Local calculations, worked examples, hints, copying answers and cached answers use no solves.

Technical failures return the reserved solve. An automatic retry is included in the same submission. A new successful AI submission counts again, even if it follows an earlier answer.

Step-by-step hints

Try:

Worked example

Step-by-step solution

$6x^2 + 11x - 10$

Step 1 / 4

Check for a common factor

6, 11 and 10 share no common factor, so move on.

How to use the Factoring Calculator

Type a polynomial and this factoring calculator factors it completely over the integers, naming the pattern it uses at each step and multiplying back at the end to prove the answer is right.

Enter the expression to factor, for example 6x² + 11x − 10.
Press Solve it. The calculator first pulls out any greatest common factor.
It then picks the pattern that fits: trinomial (ac method), difference of squares, sum or difference of cubes, or grouping.
The last step multiplies the factors back together as a check.

Factoring with the ac method

a^2 - b^2 = (a - b)(a + b)

To factor ax² + bx + c, find two numbers that multiply to a·c and add to b. Split the middle term with those numbers, then factor by grouping. If no such integers exist, the trinomial is prime over the integers.

Always look for a greatest common factor first; it makes every later step easier. Special products such as a² − b² = (a − b)(a + b) are worth recognizing on sight.

Factoring calculator example: a difference of cubes

x^3-27=(x-3)(x^2+3x+9)

For x³ − 27, recognize that both terms are cubes: x³ is the cube of x and 27 is the cube of 3. Apply a³ − b³ = (a − b)(a² + ab + b²), with a = x and b = 3. The first factor is x − 3; the second is x² + 3x + 9. This pattern handles a cubic expression without guessing several pairs of numbers.

Check the factoring calculator result by multiplying the two factors. The middle terms cancel and the product returns x³ − 27. Factoring rewrites the original expression as a product. If your exercise instead asks you to solve x³ − 27 = 0 over the real numbers, the real solution is x = 3. State that extra equation and number domain before turning factors into solutions.

Factoring calculator example: squares and a common factor

4x^3-36x=4x(x^2-9)=4x(x-3)(x+3)

The expression 4x² − 9y² is a difference of squares, because its terms are (2x)² and (3y)². Using a² − b² = (a − b)(a + b) gives (2x − 3y)(2x + 3y). A plus sign between the original squares would require a different analysis; do not apply the difference-of-squares rule to a sum.

For 4x³ − 36x, first remove the greatest common factor, 4x. The remaining expression is x² − 9, so apply the same square pattern to obtain 4x(x − 3)(x + 3). Keeping the common factor in the final answer is essential: omitting 4x changes the polynomial. Multiply the complete product to verify both the leading term and the constant or lower-degree terms.

Frequently asked questions

What does it mean to factor completely?

Every factor is prime: none of them can be factored further over the integers. For example 2x² − 8 = 2(x − 2)(x + 2), not just 2(x² − 4).

Can it factor polynomials with two variables?

Yes. Expressions such as 4x² − 9y² or x² + 5xy + 6y² use the same patterns with both variables.

What if a polynomial cannot be factored?

The calculator explains why, for example when no integer pair multiplies to ac and adds to b, and states that the polynomial is prime over the integers.

Have a different kind of math problem? Try the free math solver. Use the subject menu for physics and chemistry.