hey everybody, this is my first post on the forum. I'm on my trig+ summer assignment and I only need help on one problem. The gist of it is that there's a graph, and you need to find the equation for the polynomial on the graph (I've attached a picture of the graph). Here's what I've done so far:

I put all the x intercepts in the numerator, vertical asymptotes in the denominator, and (x-5) in both because it's a hole. Then, to get it to equal the point (5, -756/25), I put in "a" and set the equation equal to -756/25. Then I got "a", factored, factored, factored, and got an answer (numerator over denominator), but it didn't work. It seems like the polynomial is fifth degree because of the turning points and end behavior, but I can't find enough factors to "fill up" the numerator and/or denominator to said fifth degree. SO, I'm positive that I've done everything that I know how to do...anybody have any thoughts? Thanks again.

Oh, and PS: My best answer was (-72x^3+936x^2+576x-17280)/(x^3-10x^2-125x+750)