4. Show two different ways to factor \( -12 x+24-18 y \).

Certainly! Let's factor the expression \( -12x + 24 - 18y \) in two different ways by identifying different greatest common factors (GCF) and organizing the terms accordingly. ### **Method 1: Factoring Out 6** 1. **Identify the GCF:** - The coefficients are -12, 24, and -18. - The greatest common factor (GCF) of 12, 24, and 18 is **6**. 2. **Factor out 6:** \[ -12x + 24 - 18y = 6(-2x + 4 - 3y) \] - **Explanation:** - \(-12x ÷ 6 = -2x\) - \(24 ÷ 6 = 4\) - \(-18y ÷ 6 = -3y\) 3. **Final Factored Form:** \[ 6(-2x + 4 - 3y) \] ### **Method 2: Factoring Out -6** 1. **Identify an Alternative GCF:** - Sometimes, factoring out a negative GCF can simplify the expression or make certain properties clearer. - Here, we choose **-6**. 2. **Factor out -6:** \[ -12x + 24 - 18y = -6(2x - 4 + 3y) \] - **Explanation:** - \(-12x ÷ -6 = 2x\) - \(24 ÷ -6 = -4\) - \(-18y ÷ -6 = 3y\) 3. **Final Factored Form:** \[ -6(2x - 4 + 3y) \] ### **Summary** - **First Factoring:** \( 6(-2x + 4 - 3y) \) - **Second Factoring:** \( -6(2x - 4 + 3y) \) Both methods correctly factor the original expression but use different common factors, providing flexibility depending on the context or preferred form.