Greatest common factor
Factor 6x^3+9x^2
Method: Extract the largest shared numerical and variable factor.
- 1The numerical GCF of 6 and 9 is 3.
- 2Both terms contain x^2.
- 3Divide each term by 3x^2 to form the remaining binomial.
Final answer
Free online calculator
Factoring Calculator
Factor polynomials, quadratics, and expressions using GCF, grouping, difference of squares, and other methods.
Step-by-step solutions
Clear, detailed explanations
Instant results
Accurate answers in seconds
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How to Use the Factoring Calculator
1
Enter the expression
Type the polynomial you want to factor.
2
Identify the method
We detect GCF, grouping, or special-product patterns.
3
Verify by expanding
The result is checked by expanding back to the original expression.
Example
How the Factoring Calculator Chooses a Method
Rewrite a polynomial as a product and see which common factor or identity makes the factorization possible.
The calculator checks the greatest common factor first, then standard identities, trinomial patterns, and grouping. A factorization is verified by expanding the product back to the original expression.
Supported problem types
- Greatest-common-factor extraction
- Difference of squares and perfect-square identities
- Common quadratic and polynomial factorizations
Limits and assumptions
- Some polynomials are irreducible over the requested number system.
- Factoring over real numbers can differ from factoring over complex numbers.
Worked Factoring Calculator Examples
Each example names the method, shows the ordered reasoning, and keeps the final answer separate so you can check your own work.
Difference of squares
Factor x^2-16
Method: Use a^2-b^2.
- 1Recognize 16 as 4^2.
- 2Apply (a-b)(a+b).
- 3Expand to verify the middle terms cancel.
Final answer
Quadratic trinomial
Factor x^2+7x+12
Method: Find two integers with product 12 and sum 7.
- 1List factor pairs of 12.
- 2Choose 3 and 4 because 3+4=7.
- 3Write the matching binomials.
Final answer
Learn This Topic
What the Factoring Calculator Helps You Understand
Factor polynomials, quadratics, and expressions using GCF, grouping, difference of squares, and other methods.
Learning focus 1
Type the polynomial you want to factor.
Learning focus 2
We detect GCF, grouping, or special-product patterns.
Learning focus 3
The result is checked by expanding back to the original expression.
Input tips
- • Type the polynomial you want to factor.
- • Yes. The calculator recognizes grouping patterns and shows the intermediate groups.
Common mistakes to avoid
- • Skipping the greatest common factor before looking for another pattern.
- • Stopping before checking the factors by expanding them.
Frequently Asked Questions
Can it factor by grouping?
Yes. The calculator recognizes grouping patterns and shows the intermediate groups.
Does it handle special products?
Yes. Difference of squares, perfect-square trinomials, and sum/difference of cubes are all supported.
How do I check a factorization?
Expand the proposed factors and confirm that every coefficient matches the original polynomial.
Why should I check the GCF first?
Removing the GCF exposes the simpler remaining pattern and prevents an incomplete factorization.