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Factoring Linear Expressions
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Factoring Linear Expressions
Choose the best answer for each multiple-choice question. For the remaining problems, factor out the greatest common factor (GCF) and show your work.
Multiple Choice
1.Which expression is the factored form of 10x + 15?
- 5(2x + 3)
- 10(x + 15)
- 5x + 15
- 25x
2.What is the greatest common factor of 18y and 12?
- 3
- 6
- 9
- 12
3.Which property is used when 21a + 14 is rewritten as 7(3a + 2)?
- Commutative Property
- Associative Property
- Distributive Property
- Identity Property
4.Select every expression equivalent to 3(4x + 7).
- 12x + 21
- 6(2x + 3.5)
- 7x + 12
- 3(4x) + 7
Factor the Expressions
Factor each expression completely by finding its greatest common factor.
5.Factor 16x + 24.
6.Factor 20y − 30.
7.Factor 12a + 18b + 6.
8.A rectangular patio is 5 feet wide and has a length of (6x + 9) feet. Write an expression for its area, then factor the expression completely.
Problem Solving
9.Nia buys 4 notebooks that cost $n each and 4 folders that cost $3 each. Write an expression for the total cost and then factor it.
10.In your own words, explain one reason factoring can be useful. Include an example that shows an expression and its factored form.
11.Challenge: Factor 30pq + 18p − 12 completely. Show how you found the GCF.
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