1. **State the problem:** Simplify the quadratic expression $2x^2 + 18x + 28$ by factoring. 2. **Formula and rules:** To factor a quadratic expression $ax^2 + bx + c$, look for the greatest common factor (GCF) first. 3. **Find the GCF:** The coefficients are 2, 18, and 28. The GCF is 2. 4. **Factor out the GCF:** $$2x^2 + 18x + 28 = 2(x^2 + 9x + 14)$$ 5. **Factor the quadratic inside the parentheses:** Find two numbers that multiply to 14 and add to 9. These are 7 and 2. 6. **Write the factored form:** $$2(x^2 + 9x + 14) = 2(x + 7)(x + 2)$$ 7. **Final answer:** The factored form of $2x^2 + 18x + 28$ is $$\boxed{2(x + 7)(x + 2)}$$