1. **State the problem:** Factor completely the quadratic expression $5x^2 - 50x + 120$. 2. **Identify the greatest common factor (GCF):** The coefficients 5, -50, and 120 all share a GCF of 5. 3. **Factor out the GCF:** $$5x^2 - 50x + 120 = 5(x^2 - 10x + 24)$$ 4. **Factor the quadratic inside the parentheses:** We need two numbers that multiply to $24$ and add to $-10$. 5. **Find the pair:** The numbers are $-6$ and $-4$ because $-6 \times -4 = 24$ and $-6 + (-4) = -10$. 6. **Write the factored form:** $$5(x - 6)(x - 4)$$ **Final answer:** $5(x - 6)(x - 4)$