Question
31. Critique Reasoning Chris says that the expression \( 4 n-2 \) can be written as \( 2(2 n-1) \). Do you agree? Explain.
Ask by Lyons Ramos. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Yes, Chris is correct. The expression \(4n - 2\) can be factored as \(2(2n - 1)\) by factoring out the greatest common factor of 2 from both terms.
Solution
Yes, I agree with Chris's reasoning. Here's why:
**Original Expression:**
\(4n - 2\)
**Factoring Out the Greatest Common Factor (GCF):**
To factor the expression, identify the greatest common factor of the terms involved.
- The first term is \(4n\), and the second term is \(-2\).
- The GCF of 4 and 2 is **2**.
**Factored Form:**
Factor out the GCF (2) from each term:
\[
4n - 2 = 2(2n) - 2(1) = 2(2n - 1)
\]
**Verification:**
To ensure the factoring is correct, you can distribute the 2 back into the parentheses:
\[
2(2n - 1) = 2 \times 2n + 2 \times (-1) = 4n - 2
\]
This matches the original expression.
**Conclusion:**
Chris correctly factored the expression \(4n - 2\) as \(2(2n - 1)\). The factoring process involves identifying and extracting the greatest common factor, which in this case is 2.
Reviewed and approved by the UpStudy tutoring team
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Absolutely, I agree with Chris! The expression \( 4n - 2 \) can indeed be factored into \( 2(2n - 1) \). If you distribute the \( 2 \) in \( 2(2n - 1) \), you get \( 2 \times 2n - 2 \times 1 \), which simplifies back to \( 4n - 2 \). So, Chris has correctly demonstrated a valid algebraic transformation! It’s like magic when you factor! But remember, a common mistake when factoring is forgetting to distribute correctly. Always double-check your work by distributing your factored form back to the original expression. It's a simple habit that can save you from potential errors in more complex problems down the line!
