1. **State the problem:** Factor the quadratic expression $2x^2 - 6x - 8$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate:** Here, $a=2$, $b=-6$, and $c=-8$. Calculate $a \times c = 2 \times (-8) = -16$. 4. **Find two numbers:** We need two numbers that multiply to $-16$ and add to $-6$. These numbers are $-8$ and $2$. 5. **Rewrite the middle term:** Rewrite $-6x$ as $-8x + 2x$: $$2x^2 - 8x + 2x - 8$$ 6. **Group terms:** Group the terms: $$(2x^2 - 8x) + (2x - 8)$$ 7. **Factor each group:** $$2x(x - 4) + 2(x - 4)$$ 8. **Factor out the common binomial:** $$(2x + 2)(x - 4)$$ 9. **Factor out the common factor in the first binomial:** $$2(x + 1)(x - 4)$$ **Final answer:** $$2(x + 1)(x - 4)$$