📚 Topic Summary
Factoring polynomials is the process of breaking down a polynomial expression into a product of simpler expressions (factors). These factors, when multiplied together, give you back the original polynomial. Finding the Greatest Common Factor (GCF) involves identifying the largest factor that divides all terms in the polynomial. Factoring by grouping is useful when dealing with polynomials with four or more terms, where you group terms together that share common factors, and then factor out those common factors.
🧮 Part A: Vocabulary
Match the term to its definition:
| Term |
Definition |
| 1. Greatest Common Factor (GCF) |
A. A polynomial with four or more terms that can be factored by grouping terms with common factors. |
| 2. Factoring |
B. To express a polynomial as a product of two or more polynomials. |
| 3. Polynomial |
C. The largest factor that divides all terms in a polynomial. |
| 4. Factor by Grouping |
D. An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. |
| 5. Factor |
E. A number or expression that divides evenly into another number or expression. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph:
When factoring polynomials, it's always a good idea to first look for a __________. If a polynomial has four terms, you might be able to use __________ to factor it. This involves grouping terms that share a common __________, and then factoring out those common factors. Always check your answer by __________ the factors to make sure you get the original polynomial.
🤔 Part C: Critical Thinking
Explain in your own words why finding the GCF is an important first step when factoring polynomials. Provide an example to support your answer.