Common Monomial Factor Formula
Master the art of factoring polynomials using the greatest common factor
What is a Common Monomial Factor?
A common monomial factor is the largest monomial that divides evenly into each term of a polynomial expression.
When we factor out the common monomial factor, we use the distributive property in reverse.
General Formula
Where GCF is the Greatest Common Factor of all terms
Step-by-Step Process
Step 1: Identify the GCF
Find the greatest common factor of all coefficients and the lowest power of each variable present in all terms.
Step 2: Divide Each Term
Divide each term of the polynomial by the GCF to find the remaining factors.
Step 3: Write the Factored Form
Express the polynomial as the product of the GCF and the remaining polynomial.
Worked Examples
Example 1: Simple Monomial Factor
Factor:
GCF:
Solution:
Example 2: Multiple Variables
Factor:
GCF:
Solution:
Example 3: Higher Degree Terms
Factor:
GCF:
Solution:
Key Points to Remember
- Always look for the greatest common factor first when factoring polynomials
- The GCF must be a factor of every term in the polynomial
- Include both numerical coefficients and variable factors in the GCF
- Use the lowest power of each variable that appears in all terms
- Always check your answer by expanding the factored form
Practice Problems
Try factoring these expressions: