📚 Topic Summary
Factoring monomials involves expressing a single-term algebraic expression as a product of its factors. These factors can be numbers, variables, or a combination of both. Understanding the prime factorization of coefficients and applying exponent rules are key to successful monomial factoring. It's a foundational skill for simplifying algebraic expressions and solving equations.
Essentially, we are trying to find what multiplied together gives us the original monomial. Think of it like un-distributing!
🧠 Part A: Vocabulary
Match the term with its correct definition:
| Term |
Definition |
| 1. Coefficient |
A. A term with only a number and no variables. |
| 2. Variable |
B. A symbol (usually a letter) representing an unknown value. |
| 3. Constant |
C. The number that multiplies the variable in an algebraic term. |
| 4. Monomial |
D. An expression with only one term. |
| 5. Factor |
E. Numbers or expressions that when multiplied produce a given number or expression. |
Match the following: 1-C, 2-B, 3-A, 4-D, 5-E
📝 Part B: Fill in the Blanks
Factoring a monomial involves breaking it down into its __________. The __________ is the numerical part of the monomial, while the __________ represents the unknown value. To factor, find the prime factorization of the coefficient and express the variable with its respective __________. Understanding these concepts is crucial for simplifying __________ expressions.
Answer Key: factors, coefficient, variable, exponent, algebraic
💡 Part C: Critical Thinking
Explain in your own words why factoring monomials is a useful skill in algebra. Provide an example of a situation where it might be helpful.