1. **State the problem:** Simplify or solve the quadratic expression $2x^2 + 4x - 16$. 2. **Identify the formula and rules:** This is a quadratic expression of the form $ax^2 + bx + c$ where $a=2$, $b=4$, and $c=-16$. 3. **Factor the expression:** First, factor out the greatest common factor (GCF) from all terms. $$2x^2 + 4x - 16 = 2(x^2 + 2x - 8)$$ 4. **Factor the quadratic inside the parentheses:** Find two numbers that multiply to $-8$ and add to $2$. These numbers are $4$ and $-2$. $$x^2 + 2x - 8 = (x + 4)(x - 2)$$ 5. **Write the fully factored form:** $$2(x + 4)(x - 2)$$ 6. **Explanation:** We factored out the common factor 2 first, then factored the quadratic trinomial into two binomials. **Final answer:** $$2(x + 4)(x - 2)$$