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

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.