📚 Topic Summary
Factoring by grouping is a technique used when you have a polynomial with four terms. The basic idea is to pair the terms, factor out the greatest common factor (GCF) from each pair, and then, if you're lucky, you'll have a common binomial factor that you can factor out. This leaves you with a factored form of the original polynomial.
For example, consider the polynomial $ax + ay + bx + by$. We can group the first two terms and the last two terms: $(ax + ay) + (bx + by)$. Then, we factor out the GCF from each group: $a(x + y) + b(x + y)$. Notice that $(x + y)$ is a common factor. We can factor it out to get $(x + y)(a + b)$.
🧠 Part A: Vocabulary
Match the following terms with their definitions:
| Term |
Definition |
| 1. Polynomial |
A. The greatest factor that divides two or more numbers. |
| 2. Factor |
B. A term or expression that is multiplied by another to produce a product. |
| 3. Grouping |
C. An expression with more than two terms. |
| 4. GCF |
D. A technique used to factor polynomials with four or more terms. |
| 5. Binomial |
E. An expression with two terms. |
✏️ Part B: Fill in the Blanks
Factoring by ________ is used when a polynomial has four ________. The first step is to ________ the polynomial into two groups of two ________. Then, find the ________ ________ ________ (GCF) of each group. If the remaining binomials are ________, factor out the common ________. This will provide the ________ answer.
🤔 Part C: Critical Thinking
Explain in your own words why factoring by grouping works. Provide an example polynomial and show each step of the factoring process.