One solution to x³ - 2x² - 5x + 6 = 0 is x = 1. What is the sum of the other two solutions?

Since $x=1$ is a root, divide by $(x-1)$ to get $x^2-x-6=(x-3)(x+2)$, so the other roots are $3$ and $-2$. Their sum is $3+(-2)=1$, choice F. A faster check uses Vieta's formulas: the three roots sum to $2$ (the opposite of the $x^2$ coefficient), and $2-1=1$. Choice G, $-1$, reverses the sign of the sum. Choice H, $5$, is the difference $3-(-2)$ rather than the sum. Choice J, $-6$, is the product of the two roots (and the constant term of the quotient), not their sum.