📚 Topic Summary
Finding the Greatest Common Factor (GCF) of monomials is a fundamental skill in algebra. It involves identifying the largest expression that divides evenly into two or more monomials. This expression includes both numerical coefficients and variable factors with exponents. For numerical coefficients, find the largest number that divides all the coefficients. For the variables, identify common variables and choose the smallest exponent of each common variable.
In essence, you're deconstructing each monomial into its prime factors and variable components, then reconstructing the GCF using only the common elements raised to the lowest power present in any of the original monomials. This ensures the GCF can indeed divide into each original term without leaving a remainder.
🧠 Part A: Vocabulary
| Term |
Definition |
| 1. Monomial |
a. The largest factor that divides two or more terms. |
| 2. Coefficient |
b. A number multiplied by a variable. |
| 3. Variable |
c. A symbol representing an unknown quantity. |
| 4. Exponent |
d. An expression with one term. |
| 5. Greatest Common Factor |
e. The power to which a number or variable is raised. |
Match each term with its definition.
📝 Part B: Fill in the Blanks
The GCF of monomials involves finding the largest factor that divides into all terms. The numerical part of the monomial is called the _____. When finding the GCF, select the _____ exponent of each common variable. A _____ is an algebraic expression containing only one term. The GCF will always _____ each term in the original expression evenly. Factoring out the GCF _____ the expression.
💡 Part C: Critical Thinking
Explain, in your own words, how finding the GCF of monomials can simplify algebraic expressions. Provide an example.