What is limit of f(x) = (x^3-2x^2-9x+4)/(x^2-2x-8) as x approaches 4

First notice that . If is not a factor of the numerator, then there is a non-removable discontinuity at , and a removable discontinuity otherwise.

You have , which means, by the polynomial remainder theorem, that is indeed a linear factor of the numerator. Dividing yields a quotient of



so the limit is