Calculator
Example data table
These sample inputs show common factoring patterns.
| # | Input expression | Expected GCF | Example factored form |
|---|---|---|---|
| 1 | 6x^2y - 9xy^2 + 3xy | 3xy | 3xy(2x - 3y + 1) |
| 2 | 12a^3b + 18a^2b^2 - 6a^4 | 6a^2 | 6a^2(2ab + 3b^2 - a^2) |
| 3 | 15p^2q + 10pq^3 | 5pq | 5pq(3p + 2q^2) |
Formula used
- Numeric GCF: \(\gcd(|c_1|, |c_2|, \dots, |c_n|)\), where \(c_i\) are term coefficients.
- Variable part: for each variable \(v\), use \(\min(e_{1v}, e_{2v}, \dots, e_{nv})\).
- Factoring: \(\text{Expression} = \text{GCF} \times (\text{each term} \div \text{GCF})\).
If a term is missing a variable, its exponent is treated as 0 for that variable.
How to use this calculator
- Type your polynomial using + and - between terms.
- Write variables as letters, like x, y, a, or m.
- Add exponents with a caret, like x^3 or y^2.
- Press Factor Now to compute the shared monomial.
- Review the detected-term table and the step list.
- Use Download CSV or Download PDF for reports.
FAQs
1) What does monomial factoring mean?
It means pulling out the greatest common monomial shared by every term. This simplifies the expression and can be the first step before deeper factoring methods.
2) What is the “greatest common monomial” here?
It is the product of the greatest common divisor of coefficients and every variable raised to the smallest exponent that appears in all terms.
3) Can I factor an expression with constants only?
Yes. The variable part becomes 1, and the GCF is simply the gcd of the numbers. The result is that GCF times a simpler constant expression.
4) What if a variable is missing from one term?
Then that variable cannot be part of the common monomial, because its exponent is treated as 0 for that term. The calculator automatically handles this rule.
5) Does it support decimal coefficients?
Yes. The calculator uses a shared power-of-ten scaling to compute a numeric GCF, then scales back. For clean results, integers are still recommended when possible.
6) Why do I see parentheses in the final form?
Factoring writes the expression as GCF multiplied by what remains. Parentheses clearly show the remaining polynomial being multiplied by the extracted monomial.
7) My output looks different from a textbook. Is it wrong?
Not necessarily. Factored forms can be equivalent with different ordering or sign choices. Multiply the GCF back through the parentheses to verify it matches the original expression.
Tip: Use consistent variable letters and integer exponents for best results.