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The image you provided contains a mathematical activity focused on simplifying polynomials and identifying factors.

Here’s a breakdown of the activity:

### 1. Questions (at the top of the image):
- **What did you do to reduce each fraction to its simplest form?**
- **When can you say that a fraction is already in its simplest form?**

These questions are likely aimed at guiding students through the process of reducing algebraic fractions by factoring and canceling common factors.

### 2. Table: Let Go and Be Unique!
This table presents a task where pairs of polynomials are provided, and students are required to:
- **Factor** the given polynomials.
- Identify the **common factor** between the polynomials (in the “Let Go” column).
- Identify the **unique factor** for each polynomial that is not shared (in the “Be Unique” column).

#### Example:
- **Item No. 1 (Given):** 
   \[
   x^2 + x - 6 \quad \text{and} \quad x^2 - 9
   \]
   - **Factored Form:**
      - \(x^2 + x - 6 = (x - 2)(x + 3)\)
      - \(x^2 - 9 = (x - 3)(x + 3)\)
   - **Let Go:** \(x + 3\) (common factor)
   - **Be Unique:** \(x - 2\) and \(x - 3\)

#### Additional Polynomials in the Table (Items 2-5):
Students need to factor the remaining polynomials in the table and complete the "Let Go" and "Be Unique" columns.

- **Item 2:** 
   - Given: \(15a\) and \(12a^2b\)
- **Item 3:**
   - Given: \(3x^2 - 12x\) and \(6x^2 + 3x\)
- **Item 4:** 
   - Given: \(x^2 + 4x + 3\) and \(x^2 - 3x - 4\)
- **Item 5:** 
   - Given: \(2x^2 + 11x + 5\) and \(x^2 + 6x + 5\)

### Guide Questions:
1. What techniques did you use to identify the factors of the given polynomials?
2. If you are going to write the remaining factors in the Be Unique column as rational expressions, are these rational expressions in simplest form? Why or why not?

### Next Steps:
Would you like me to factor the polynomials in the table for you and complete the columns? Let me know if you'd like any specific clarifications!

Here are some relative questions to expand on this topic:
1. How do you factor a quadratic expression?
2. What is the difference between a common factor and a unique factor?
3. Can two completely different polynomials have the same factors?
4. Why is factoring important in simplifying algebraic expressions?
5. How can you verify if your factorization is correct?

#### Tip:
When factoring polynomials, always check for the greatest common factor (GCF) first before attempting other methods like grouping or the quadratic formula.

Factor polynomials, identify common and unique factors in given pairs of polynomials.

Learn how to factor polynomials and identify the common and unique factors in given pairs of quadratic expressions. This activity focuses on factoring techniques, algebraic expressions, and rational algebra. Suitable for students in Grades 9-10.

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