The polynomial x³ - 7x + 6 has x = 1 as one of its roots. What is the sum of the other two roots?

Since $x = 1$ is a root, $x - 1$ divides the polynomial. Dividing $x^3 + 0x^2 - 7x + 6$ by $x - 1$ gives $x^2 + x - 6$, which you can verify by multiplying back. The other two roots solve $x^2 + x - 6 = 0$, which factors as $(x+3)(x-2) = 0$, so the roots are $-3$ and $2$. Their sum is $-3 + 2 = -1$, which matches Vieta's formula: the sum is the negative of the $x$-coefficient, $-1$. A common wrong answer is 1, from forgetting the negative sign, and another is $-6$, which is the product.