Calculator Form
Example Data Table
This table shows sample expressions and the common monomial each one produces.
| Sample expression | Greatest common monomial | Factored form |
|---|---|---|
| 12x^3y^2 + 18x^2y^5 - 6x^4y | 6x^2y | 6x^2y(2xy + 3y^4 - x^2) |
| 20m^4n^2 - 35m^2n^5 + 10m^3n | 5m^2n | 5m^2n(4m^2n - 7n^4 + 2m) |
| -15a^3b^2 + 25a^2b^4 - 10ab | 5ab | 5ab(-3a^2b + 5ab^3 - 2) |
Formula Used
Step 1: Find the greatest common divisor of the coefficients.
Step 2: For each variable shared by every term, select the smallest exponent.
Step 3: Multiply the coefficient GCD by every shared variable raised to its minimum exponent.
Step 4: Divide each original term by the common monomial and place the quotients inside parentheses.
How to Use This Calculator
- Enter a polynomial with two or more terms.
- Write coefficients as integers and exponents as whole numbers.
- Set your preferred variable order for cleaner output.
- Choose whether the common factor stays positive or matches the first term.
- Press Factor Expression to show the result above the form.
- Review the simplified factorization, exponent table, and Plotly chart.
- Use the CSV and PDF buttons to export your results.
Frequently Asked Questions
1. What does this calculator factor out?
It extracts the greatest common monomial from all terms in the entered polynomial. That factor includes the coefficient GCD and every variable power shared by every non-zero term.
2. Can I enter negative terms?
Yes. Negative coefficients are supported. You can also choose whether the extracted common factor remains positive or follows the sign of the first non-zero term.
3. Are decimal coefficients supported?
This version is designed for integer coefficients. Integer input keeps the greatest common divisor exact and makes the factored result easier to verify in algebra practice.
4. What happens when no non-trivial monomial exists?
The calculator still evaluates the expression, but it reports that no non-trivial common monomial exists. In that case, the common factor is effectively 1.
5. Why does the graph only track exponents?
The graph focuses on variable powers because exponent comparison decides the variable portion of the common monomial. Coefficient factoring is already summarized numerically above the chart.
6. Can repeated variables in one term be combined?
Yes. A term such as x^2x^3 is interpreted as x^5 during parsing. The calculator combines repeated variable powers before finding the common monomial.
7. Why should I set a variable order?
Variable order does not change the algebra. It only changes the display format so your output can match a classroom convention, textbook style, or personal preference.
8. Can I use the exported files for homework review?
Yes. The CSV file stores a quick summary and exponent matrix, while the PDF file produces a neat report containing the main factorization results.