The polynomial x³ - 2x² - 5x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?

Since $x = 1$ is a root, $x - 1$ is a factor. Dividing gives $x^3 - 2x^2 - 5x + 6 = (x - 1)(x^2 - x - 6)$, which you can confirm by multiplying. The other roots solve $x^2 - x - 6 = 0$, which factors as $(x - 3)(x + 2) = 0$, so they are 3 and $-2$. Their sum is $3 + (-2) = 1$, choice D, matching Vieta's formula: the sum is the negative of the $x$-coefficient, $-(-1) = 1$. Choice A ($-1$) forgets to flip the sign. Choice B (2) is the cubic's $x^2$-coefficient with the sign flipped. Choice C (6) is the constant term.