Recall that a rational function:
has a vertical asymptote at x₀ if and only if:
Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
Finally, since the rational function has y-intercept at (0,2) we get that:
Simplifying the above equation we get:
Dividing the above equation by 4 we get:
Therefore, the rational function that satisfies the given conditions is:
Answer:
The numerator is:
The denominator is: