31. Critique Reasoning Chris says that the expression $$ 4 n-2 $$ can be written as $$ 2(2 n-1) $$. Do you agree? Explain.

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UpStudy AI · Accepted Answer

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.
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.

Critique Reasoning Chris says that the
expression can be written as .
Do you agree? Explain.

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Critique Reasoning Chris says that the expression can be written as . Do you agree? Explain.