📚 Part 1: Multiple Choice

1. Which expression shows the factored form of 6x + 9?

3(2x + 3)

6(x + 9)

3x + 9

15x

2. What is the greatest common factor (GCF) of 12y and 8?

2

4

8

12

3. Which property is used when factoring 15a + 10 as 5(3a + 2)?

Commutative Property

Associative Property

Distributive Property

Identity Property

4. Check all expressions that are equivalent to 4(2x + 5):

8x + 20

6x + 9

2(4x + 10)

4x + 20

✏️ Part 2: Factor the Expressions

5. Factor: 14x + 21

6. Factor: 18y - 12

7. Factor: 9a + 15b + 6

8. Real-World Problem: A rectangular garden has a length of (8x + 12) feet. If the width is 4 feet, write an expression for the area and then factor it completely.

Area = length × width = _____________ × 4 = _____________

Factored form: _____________

🎯 Part 3: Problem Solving

9. Maria is buying supplies for her art class. She buys 6 paintbrushes at $x each and 6 canvases at $8 each. Write an expression for her total cost, then factor it.

Total cost expression: _____________

Factored form: _____________

10. Explain in your own words: Why is factoring useful when working with algebraic expressions? Give an example.

11. Challenge: Factor 24mn + 16m - 8. Show all your work and explain each step.