Question 411181
It's fairly tedious listing all positive/negative factors of -1800 so I'll solve using the quadratic formula. The roots of {{{x^2 - 200x - 1800}}} are


{{{x = (200 +- sqrt(40000 - 4(-1800)))/2 = (200 +- sqrt(47200))/2 = 100 +- 10sqrt(118)}}}. Therefore the polynomial can be factored as {{{(x - (100+10sqrt(118)))(x - (100-10sqrt(118)))}}}. However, it's still a pretty ugly expression, and the polynomial cannot be factored over the integers.