In a larger picture, I am actually trying to figure out whether the graph crosses or touches the x-axis at each x-intercept. Teaching myself out of the book is proving to be a real pain...

EDIT: I want to say that the X intercepts are X=-1/2 and X=-4 but I am not positive. is the -2, ^2, and ^3 insignificant when finding the x intercepts?

Also.. Since the problem as a whole is a degree of 5, does this mean that the function will have 5 turning points?