Question: Write the following expression in factored form.
6x^2 - 5x - 4
(2x - 1)(3x + 4)
(top-left)
(x + 1)(6x - 4)
(top-left)
(2x + 1)(3x - 4)
(top-left)
(x - 1)(6x + 4)
(top-left)
1. **State the problem:** Factor the quadratic expression $$6x^2 - 5x - 4$$ into the product of two binomials.
2. **Recall the factoring method:** For a quadratic $$ax^2 + bx + c$$, find two numbers that multiply to $$a \times c$$ and add to $$b$$.
3. Here, $$a = 6$$, $$b = -5$$, and $$c = -4$$.
4. Calculate $$a \times c = 6 \times (-4) = -24$$.
5. Find two numbers that multiply to $$-24$$ and add to $$-5$$. These numbers are $$-8$$ and $$3$$ because $$-8 \times 3 = -24$$ and $$-8 + 3 = -5$$.
6. Rewrite the middle term using these numbers:
$$6x^2 - 8x + 3x - 4$$
7. Group terms:
$$(6x^2 - 8x) + (3x - 4)$$
8. Factor each group:
$$2x(3x - 4) + 1(3x - 4)$$
9. Factor out the common binomial:
$$(2x + 1)(3x - 4)$$
10. **Final answer:** The factored form of $$6x^2 - 5x - 4$$ is $$\boxed{(2x + 1)(3x - 4)}$$.