Question

Which of the following are holes of the function?
f(x)= 3(x-1(x+2)(x+3)/(x-1)^2(x+2)(x-3)(x-4)
Select all that apply

x = 1

x = –2

x = 3

x = 4

Answer 1

Interpreting
f(x) = 3(x−1)(x+2)(x+3) / [(x−1)^2(x+2)(x−3)(x−4)],

cancel common factors (x+2) and one (x−1) to get the reduced form
g(x) = 3(x+3) / [(x−1)(x−3)(x−4)].

The original function is undefined at x = 1, −2, 3, 4. A hole occurs where a factor cancels completely — that is x = −2. The others (x = 1, 3, 4) remain in the denominator and are vertical asymptotes, not holes.

Answer: x = −2 only.