1. **State the problem:** Simplify the quadratic expression $48x^2 - 200x + 200$ by factoring out the greatest common factor (GCF). 2. **Identify the GCF:** The coefficients are 48, 200, and 200. The GCF of 48, 200, and 200 is 4. 3. **Factor out the GCF:** $$48x^2 - 200x + 200 = 4(\cancel{12}x^2 - \cancel{50}x + \cancel{50})$$ Here, we cancel the factor 4 from each term inside the parentheses. 4. **Simplify inside the parentheses:** $$4(12x^2 - 50x + 50)$$ 5. **Check if the quadratic inside can be factored further:** The quadratic $12x^2 - 50x + 50$ can be simplified by factoring out 2: $$4 \times 2 (6x^2 - 25x + 25) = 8(6x^2 - 25x + 25)$$ 6. **Final factored form:** $$8(6x^2 - 25x + 25)$$ This is the simplified form by factoring out the greatest common factor. **Answer:** $8(6x^2 - 25x + 25)$