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