1. **State the problem:** Factor the quadratic equation $$2x^2 = 3x + 35$$ into its factored form. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$2x^2 - 3x - 35 = 0$$ 3. **Use factoring method:** We look for two numbers that multiply to $$2 \times (-35) = -70$$ and add to $$-3$$. 4. The numbers are $$7$$ and $$-10$$ because $$7 \times (-10) = -70$$ and $$7 + (-10) = -3$$. 5. **Rewrite the middle term:** $$2x^2 + 7x - 10x - 35 = 0$$ 6. **Group terms:** $$(2x^2 + 7x) - (10x + 35) = 0$$ 7. **Factor each group:** $$x(2x + 7) - 5(2x + 7) = 0$$ 8. **Factor out the common binomial:** $$(x - 5)(2x + 7) = 0$$ 9. **Final factored form:** $$(x - 5)(2x + 7)$$ **Answer:** The factored form is $(x - 5)(2x + 7)$. Note: The options given include duplicates and the correct two factors are $(x - 5)$ and $(2x + 7)$.