1. **State the problem:** Factor the quadratic expression $2x^2 - 3x - 20$. 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 the product and sum:** Here, $a=2$, $b=-3$, and $c=-20$. So, $a \times c = 2 \times (-20) = -40$. We need two numbers that multiply to $-40$ and add to $-3$. 4. **Find the pair:** The numbers are $5$ and $-8$ because $5 \times (-8) = -40$ and $5 + (-8) = -3$. 5. **Rewrite the middle term:** $$2x^2 - 3x - 20 = 2x^2 + 5x - 8x - 20$$ 6. **Group terms:** $$= (2x^2 + 5x) - (8x + 20)$$ 7. **Factor each group:** $$= x(2x + 5) - 4(2x + 5)$$ 8. **Factor out the common binomial:** $$= (x - 4)(2x + 5)$$ **Final answer:** The factorization of $2x^2 - 3x - 20$ is $$(x - 4)(2x + 5)$$.