During a mission near an asteroid, Emek and Tara prepared to launch a probe through a narrow observation zone. The flight computer showed that possible launch times satisfied the polynomial equation t^3 - 9t^2 + 14t + 24 = 0, where t represented hours relative to the current time. Emek tested an integer value and found that t = 4 made the polynomial zero, so he factored out (t - 4). The remaining quadratic was t^2 - 5t - 6, which Tara factored as (t - 6)(t + 1). The three candidate times were therefore t = 4, t = 6, and t = -1. They rejected -1 because it represented an hour that had already passed. Mission data also showed that after 5 hours, the asteroid would rotate into a safer orientation, so t = 4 was too early. That left t = 6 as the only usable solution. They programmed the launch for six hours later, and the probe passed safely through the observation zone, sending back detailed images of the asteroid.