Factoring Calculator

Break a polynomial into factors using the pattern that fits, then verify by expanding.

Drag & drop or upload an image or PDF

Enter a polynomial, such as 6x^2 + 11x - 10

Try an example

Factoring reverses multiplication

To factor a polynomial, rewrite it as a product of simpler expressions. The first check is always the greatest common factor. After that, the number of terms and the exponent pattern suggest what to try.

A complete factorization should multiply back to the original polynomial. Expanding the answer is a reliable check and makes sign mistakes easy to spot.

How to use the factoring calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Difference of squares

Two perfect squares separated by subtraction factor into conjugate binomials.

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

A reliable way to work through it

Greatest common factor

Pull out the largest factor shared by every term before using any other pattern.

Trinomial factoring

Find terms whose product matches ac and whose sum matches b, then group.

Special products

Recognize differences of squares and perfect square trinomials before doing longer work.

Worked example

Factor 6x² + 11x - 10

a c = 6 (- 10) = - 60

Multiply the leading coefficient and constant.

15 + (- 4) = 11

Choose factors of -60 that add to 11.

6 x^{2} + 15 x - 4 x - 10

Split the middle term.

3 x (2 x + 5) - 2 (2 x + 5)

Factor each group.

(3 x - 2) (2 x + 5)

Factor out the shared binomial.

The complete factorization is (3x - 2)(2x + 5).

Common mistakes to check

Skipping the GCF

A result is not fully factored if all terms still share a common factor.

Using sum of squares as a real pattern

a² + b² does not factor over the real numbers in the same way as a² - b².

Not multiplying back

A quick expansion verifies the middle term and both signs.

Quadratic Equation CalculatorFind real or complex roots and see which quadratic method fits the equation.Polynomial CalculatorWork with polynomial operations, factors, roots, and remainders in one place.Simplify CalculatorCombine like terms, reduce fractions, and rewrite expressions in a cleaner equivalent form.Complete the Square CalculatorTurn a quadratic into a perfect square and use it to find vertex form or roots.

Questions students ask

Can this calculator factor trinomials when a is not 1?

Yes. It can use the AC method, grouping, or another suitable method and show the intermediate steps.

Can it factor higher-degree polynomials?

Yes. It can test common factors, grouping, substitutions, and rational roots when those methods apply.

What if a polynomial is prime?

The result will explain that it is irreducible over the chosen number system rather than forcing an invalid factorization.

Does factoring help solve equations?

Yes. Once a polynomial equation is written as a product equal to zero, the zero-product property can be used to find its roots.