1. **State the problem:** We need to find which of the given expressions is a factor of the quadratic polynomial $$2x^2 - 3x - 35$$. 2. **Recall the factoring method:** To factor a quadratic of the form $$ax^2 + bx + c$$, we look for two binomials $$(mx + n)(px + q)$$ such that $$mp = a$$, $$nq = c$$, and $$mq + np = b$$. 3. **Apply to our polynomial:** Here, $$a = 2$$, $$b = -3$$, and $$c = -35$$. 4. **Find pairs for $$a imes c = 2 imes (-35) = -70$$ that sum to $$b = -3$$:** The pairs are $$7$$ and $$-10$$ because $$7 + (-10) = -3$$. 5. **Rewrite the middle term:** $$2x^2 + 7x - 10x - 35$$ 6. **Group terms:** $$(2x^2 + 7x) + (-10x - 35)$$ 7. **Factor each group:** $$x(2x + 7) - 5(2x + 7)$$ 8. **Factor out the common binomial:** $$(2x + 7)(x - 5)$$ 9. **Conclusion:** The factors of $$2x^2 - 3x - 35$$ are $$(2x + 7)$$ and $$(x - 5)$$. 10. **Check options:** Among the options, $$2x + 7$$ is a factor. **Final answer:** $$2x + 7$$ is a factor of $$2x^2 - 3x - 35$$.