1. **State the problem:** We need to find which binomial is a factor of the quadratic expression $$2x^2 + x - 1$$. 2. **Recall the factoring method:** To factor a quadratic $$ax^2 + bx + c$$, we look for two binomials $$(mx + n)(px + q)$$ such that $$mp = a$$, $$nq = c$$, and $$mq + np = b$$. 3. **Apply to our expression:** Here, $$a=2$$, $$b=1$$, and $$c=-1$$. 4. **Find factor pairs of $$a imes c = 2 imes (-1) = -2$$:** The pairs are $$(2, -1)$$ and $$(-2, 1)$$. 5. **Find pair that sums to $$b=1$$:** The pair $$2$$ and $$-1$$ sums to $$1$$. 6. **Rewrite the middle term:** $$2x^2 + 2x - x - 1$$ 7. **Group terms:** $$(2x^2 + 2x) - (x + 1)$$ 8. **Factor each group:** $$2x(x + 1) - 1(x + 1)$$ 9. **Factor out common binomial:** $$(2x - 1)(x + 1)$$ 10. **Check which binomial is in the options:** The binomials are $$2x - 1$$ and $$x + 1$$. 11. **Answer:** Among the options, $$2x - 1$$ is a factor of the expression. **Final answer:** $$2x - 1$$