Answer
vertical asymptote $x=1$,
horizontal asymptote $y=0$,
oblique asymptote $none$.
Work Step by Step
Step 1. Factor the function $P(x)=\frac{4x^2}{x^3-1}=\frac{4x^2}{(x-1)(x^2+x+1)}$,
Step 2. we can find the vertical asymptote $x=1$,
Step 3. we can find the horizontal asymptote $y=0$,
Step 4. we can find the oblique asymptote $none$.
