The polynomial x³ - 4x² - x + 4 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 $x^3 - 4x^2 - x + 4 = (x - 1)(x^2 - 3x - 4)$. The other roots solve $x^2 - 3x - 4 = 0$, which factors as $(x - 4)(x + 1) = 0$, so they are 4 and $-1$. Their sum is 3, matching Vieta's formula, $-(-3) = 3$. A common wrong answer is $-3$, which forgets to flip the sign. Another is 4, which is just one root, and a third is $-4$, the product of the other two roots. The sum is the opposite of the middle coefficient.