Problem: Factoring Linear Expressions
The task is to factor each of the given linear expressions. Factoring involves expressing a polynomial as a product of simpler polynomials (or monomials). Here are the steps to solve each problem:
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#### 1. \( 6x + 12 \)
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Step 1: Identify the greatest common factor (GCF) of the terms.
- The terms are \( 6x \) and \( 12 \).
- The GCF of \( 6x \) and \( 12 \) is \( 6 \).
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Step 2: Factor out the GCF.
- Write \( 6x + 12 \) as \( 6(x) + 6(2) \).
- Factor out \( 6 \): \( 6(x + 2) \).
Answer: \( 6(x + 2) \)
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#### 2. \( 8y - 4 \)
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Step 1: Identify the GCF of the terms.
- The terms are \( 8y \) and \( -4 \).
- The GCF of \( 8y \) and \( -4 \) is \( 4 \).
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Step 2: Factor out the GCF.
- Write \( 8y - 4 \) as \( 4(2y) + 4(-1) \).
- Factor out \( 4 \): \( 4(2y - 1) \).
Answer: \( 4(2y - 1) \)
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#### 3. \( 15z + 20 \)
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Step 1: Identify the GCF of the terms.
- The terms are \( 15z \) and \( 20 \).
- The GCF of \( 15z \) and \( 20 \) is \( 5 \).
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Step 2: Factor out the GCF.
- Write \( 15z + 20 \) as \( 5(3z) + 5(4) \).
- Factor out \( 5 \): \( 5(3z + 4) \).
Answer: \( 5(3z + 4) \)
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#### 4. \( 9a - 3 \)
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Step 1: Identify the GCF of the terms.
- The terms are \( 9a \) and \( -3 \).
- The GCF of \( 9a \) and \( -3 \) is \( 3 \).
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Step 2: Factor out the GCF.
- Write \( 9a - 3 \) as \( 3(3a) + 3(-1) \).
- Factor out \( 3 \): \( 3(3a - 1) \).
Answer: \( 3(3a - 1) \)
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#### 5. \( 12b + 18 \)
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Step 1: Identify the GCF of the terms.
- The terms are \( 12b \) and \( 18 \).
- The GCF of \( 12b \) and \( 18 \) is \( 6 \).
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Step 2: Factor out the GCF.
- Write \( 12b + 18 \) as \( 6(2b) + 6(3) \).
- Factor out \( 6 \): \( 6(2b + 3) \).
Answer: \( 6(2b + 3) \)
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#### 6. \( 7c - 14 \)
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Step 1: Identify the GCF of the terms.
- The terms are \( 7c \) and \( -14 \).
- The GCF of \( 7c \) and \( -14 \) is \( 7 \).
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Step 2: Factor out the GCF.
- Write \( 7c - 14 \) as \( 7(c) + 7(-2) \).
- Factor out \( 7 \): \( 7(c - 2) \).
Answer: \( 7(c - 2) \)
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Final Answers:
1. \( 6(x + 2) \)
2. \( 4(2y - 1) \)
3. \( 5(3z + 4) \)
4. \( 3(3a - 1) \)
5. \( 6(2b + 3) \)
6. \( 7(c - 2) \)
\[
\boxed{6(x + 2), 4(2y - 1), 5(3z + 4), 3(3a - 1), 6(2b + 3), 7(c - 2)}
\]
Parent Tip: Review the logic above to help your child master the concept of factoring linear expressions worksheet.
