This is how the graph, tan x looks like:
Do you notice where the graphs are trying to reach out to (at both ends)?
Similarly, we make a connection between the "factorised" terms and the graphs?
Below are some examples. Do you notice that when you express the quadratic expression into an equation (such that it is equal to zero), the answers will give the "roots" (i.e. where the curve cuts the horizontal axis).
Reference: Assignment 4.7
Set A: Questions 1 & 3
Set B: Questions 2 & 6