Quadratic Factoring 7Df136

1. **State the problem:** We need to solve the quadratic equation $$x^2 + 3x - 10 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic equation of the form $$ax^2 + bx + c = 0$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Apply the method:** Here, $$a = 1$$, $$b = 3$$, and $$c = -10$$. We need two numbers that multiply to $$1 \times (-10) = -10$$ and add to $$3$$. 4. **Find the numbers:** The numbers are $$5$$ and $$-2$$ because $$5 \times (-2) = -10$$ and $$5 + (-2) = 3$$. 5. **Rewrite the middle term:** $$x^2 + 5x - 2x - 10 = 0$$ 6. **Factor by grouping:** $$x(x + 5) - 2(x + 5) = 0$$ 7. **Factor out the common binomial:** $$(x - 2)(x + 5) = 0$$ 8. **Set each factor equal to zero:** $$x - 2 = 0 \quad \Rightarrow \quad x = 2$$ $$x + 5 = 0 \quad \Rightarrow \quad x = -5$$ 9. **Final answer:** The solutions are $$x = -5$$ and $$x = 2$$. Therefore, the correct choice is **x = -5 and x = 2**.