Calculator Input
Use whole-number coefficients. Use non-negative exponents. Terms with coefficient 0 are ignored.
Formula Used
Coefficient factor
Find the greatest common divisor of all absolute coefficients.
Variable exponents
For each variable, use the smallest exponent that appears across every non-zero term.
General factoring rule
If P = Σ aixαiyβizγiwδi, then the common monomial is gcd(|ai|)xmin(αi)ymin(βi)zmin(γi)wmin(δi).
How to Use This Calculator
- Enter up to six polynomial terms.
- Type one whole-number coefficient for each term.
- Enter the exponents for x, y, z, and w.
- Set unused terms to coefficient 0.
- Click Factor Common Monomial.
- Review the original polynomial, quotient polynomial, and factored form.
- Check the term table and graph for quick verification.
- Export the current result as CSV or PDF.
Example Data Table
Example input: 12x3y2z, 18x2y3z2, and 30x4yz.
| Term | Coefficient | x | y | z | w | Resulting Quotient Term |
|---|---|---|---|---|---|---|
| 12x3y2z | 12 | 3 | 2 | 1 | 0 | 2xy |
| 18x2y3z2 | 18 | 2 | 3 | 2 | 0 | 3y2z |
| 30x4yz | 30 | 4 | 1 | 1 | 0 | 5x2 |
Common monomial: 6x2yz
Factored form: 6x2yz(2xy + 3y2z + 5x2)
Frequently Asked Questions
1. What does this calculator factor out?
It extracts the greatest common monomial shared by every non-zero term. That includes the coefficient gcd and the minimum exponent for each listed variable.
2. Can I enter negative coefficients?
Yes. The calculator uses absolute values for the gcd, then keeps the correct signs inside the quotient polynomial after factoring.
3. What if a variable is missing from one term?
Use exponent 0 for that variable. A zero exponent means the variable is absent from that term.
4. Why are whole-number coefficients recommended?
Whole numbers make gcd-based monomial factoring clear and exact. Decimal coefficients need a different factoring approach.
5. What happens when the common factor is 1?
The tool still returns a valid result. It also tells you that no non-trivial common monomial exists across all terms.
6. How are exponents chosen for the factor?
For each variable, the calculator scans all non-zero terms and selects the smallest exponent. That minimum exponent becomes part of the shared monomial.
7. Does this fully factor the remaining polynomial?
No. This page only removes the greatest common monomial. It does not factor the quotient polynomial further.
8. What do the exports include?
The exports summarize the original expression, common factor, quotient polynomial, factored form, and the term-by-term breakdown shown on the page.