$\text { Find all the vertical asymptotes (if any) of the graph of the function } f ( x ) = \frac { x ^ { 3 } + 8 } { x + 2 } \text {. }$
A) $x = - 2$
B) $x = 8$
C) $x = 2$
D) $x = 2 , - 2$
E) no vertical asymptotes

Question

$\text { Find all the vertical asymptotes (if any) of the graph of the function } f ( x ) = \frac { x ^ { 3 } + 8 } { x + 2 } \text {. }$ 
A) $x = - 2$
B) $x = 8$
C) $x = 2$
D) $x = 2 , - 2$
E) no vertical asymptotes

Quizplus · Accepted Answer

The function $ f(x) = \frac{x^3 + 8}{x + 2} $ can be simplified because $ x^3 + 8 $ is a sum of cubes and can be factored as $ (x + 2)(x^2 - 2x + 4) $. The $ x + 2 $ terms cancel, leaving $ f(x) = x^2 - 2x + 4 $, which is a polynomial with no vertical asymptotes.