1. **State the problem:** We need to find the factored form equivalent to the quadratic expression $$2x^2 - 10x - 48$$. 2. **Write the expression:** $$2x^2 - 10x - 48$$. 3. **Factor out the greatest common factor (GCF):** The GCF of the terms is 2, so we factor it out: $$2x^2 - 10x - 48 = 2(x^2 - 5x - 24)$$ 4. **Factor the quadratic inside the parentheses:** We look for two numbers that multiply to $$-24$$ and add to $$-5$$. 5. The pair $$3$$ and $$-8$$ works because $$3 \times (-8) = -24$$ and $$3 + (-8) = -5$$. 6. **Write the factored form:** $$2(x + 3)(x - 8)$$ 7. **Check the options:** The correct factored form is $$2(x + 3)(x - 8)$$. **Final answer:** $$2(x + 3)(x - 8)$$