Question

(x^3+10x^2+31x+30)/(x^2-4)
Find vertical asymtotes, horizontal asymtotes, oblique asymtotes, and holes.

Answer 1

\[\frac{ x^3+10x^2+31x+30}{ x^2-4 }\]

Answer 2

How do I find the asymtotes and holes? I have no idea how to do this.

Answer 3

setting the denominator equal to zero will give you the holes (where the function is undefined)
setting the numerator equal to zero will give you the asymtotes (where the function is zero)

x^2-4=0
x^2=4
x=4, -4

x^3+10x^2+31x+30 = 0
factor this and you will get the asymtotes.. sorry i forgot how to factor these kinds of polynomials

Answer 4

How do I know which type of asymtote it is?

Answer 5

you do know how to factor that kind of polynomial, right? after you factor it set all the factor equal to zero and find x. you can have multiple asymtotes, i think that you will get two asymtotes.

Answer 6

Which type? Vertical/horizontal/oblique?

Answer 7

Like how do I know which are which?

Answer 8

I have (x+2)(x+3)(x+5) for the top

Answer 9

I think I remember having to like look at the factored top part and the factored bottom part and finding matches and crossing them out.

Something about asymtotes being stronger than holes.