Zero Factor Property Bce278

1. **State the problem:** We need to identify which equation is already set up for direct use of the zero-factor property and then solve it. 2. **Recall the zero-factor property:** If a product of factors equals zero, then at least one of the factors must be zero. Formally, if $$A \cdot B = 0$$ then $$A = 0$$ or $$B = 0$$. 3. **Analyze each option:** - A. $7x^2 - 32x - 15 = 0$ is a quadratic equation but not factored. - B. $(2x + 5)^2 = 3$ is not equal to zero, so zero-factor property does not apply directly. - C. $x^2 + x = 20$ is not factored and not equal to zero. - D. $(7x - 3)(x - 7) = 0$ is factored and equal to zero, so zero-factor property applies directly. 4. **Choose option D and solve:** Set each factor equal to zero: $$7x - 3 = 0$$ $$x - 7 = 0$$ 5. **Solve each equation:** For $$7x - 3 = 0$$: $$7x = 3$$ $$x = \frac{3}{7}$$ For $$x - 7 = 0$$: $$x = 7$$ 6. **Final answer:** The solutions are $$x = \frac{3}{7}$$ and $$x = 7$$. Thus, the equation set up for direct use of the zero-factor property is option D: $(7x - 3)(x - 7) = 0$ and its solutions are $x = \frac{3}{7}$ and $x = 7$.