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Factoring Linear Expressions
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Factoring Linear Expressions
📚 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.
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