1. The problem is to use the quadratic formula to factor a quadratic expression. 2. Let's consider the quadratic equation $2x^2 - 4x - 6 = 0$. 3. The quadratic formula is given by: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=2$, $b=-4$, and $c=-6$. 4. Calculate the discriminant: $$\Delta = b^2 - 4ac = (-4)^2 - 4 \times 2 \times (-6) = 16 + 48 = 64$$ 5. Find the roots: $$x = \frac{-(-4) \pm \sqrt{64}}{2 \times 2} = \frac{4 \pm 8}{4}$$ 6. Calculate each root: - For $+$ sign: $x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3$ - For $-$ sign: $x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1$ 7. Using the roots, factor the quadratic as: $$2x^2 - 4x - 6 = 2(x - 3)(x + 1)$$ 8. This shows how the quadratic formula helps find roots which are then used to factor the quadratic expression. Final answer: $2x^2 - 4x - 6 = 2(x - 3)(x + 1)$