What is the product of the two solutions to x² - 2x - 35 = 0?

Factor: $x^2 - 2x - 35 = (x - 7)(x + 5)$, since $-7 \cdot 5 = -35$ and $-7 + 5 = -2$. The solutions are $x = 7$ and $x = -5$, and their product is $7 \times (-5) = -35$, choice C. By Vieta's formulas, the product of the roots equals the constant term $c = -35$, so you can read it straight from the equation. Choice A (35) drops the sign. Choice B (2) is the sum of the roots, $7 + (-5)$. Choice D ($-2$) is the $x$-coefficient. Product means the constant term; sum means the opposite of the $x$-coefficient.