1. What is Greatest Monomial Factor?

The Greatest Monomial Factor (GMF) is the largest monomial that divides each term of a polynomial. It consists of the greatest common factor (GCF) of the coefficients and the lowest power of each variable that appears in all terms.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( GCF(coeffs) \) — Greatest common factor of all coefficients
• \( \min\_exponents(variables) \) — Variables raised to their smallest exponents across all terms

Explanation: The GMF is found by taking the GCF of the numerical coefficients and each variable raised to the smallest exponent that appears in all terms.

3. Importance of GMF Calculation

Details: Finding the GMF is the first step in factoring polynomials. It simplifies expressions and helps solve equations more efficiently.

4. Using the Calculator

Tips: Enter coefficients as comma-separated numbers, variables as comma-separated letters, and exponents as comma-separated numbers. All values must be valid.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between GCF and GMF?
A: GCF refers to numbers only, while GMF includes both numerical coefficients and variables.

Q2: Can the GMF be 1?
A: Yes, if the terms have no common factors other than 1, the GMF is 1.

Q3: How do I find the GMF for multiple terms?
A: Find the GCF of coefficients and the minimum exponent for each variable across all terms.

Q4: What if variables are different in terms?
A: Only variables common to all terms are included in the GMF.

Q5: Can the GMF include negative coefficients?
A: Typically, we use positive GMF, but technically a negative GCF could be used if all coefficients are negative.