Ok so you've figured out that a factor with power 1 (x+1) for example will cut the x axis.

A factor with power 2 (x+1)^2 for example will touch the x axis and turn back (otherwise known as a turning point)

So therefore a factor with power 3 (x+1)^3 for example will have a point of inflection on the x axis.

Now that I've told you this. Please experiment with this concept to get a good grasp on it. Go graph some graphs that have all these different types of factors

for example:

You will find that the graph will cut at -1, touch and turn at -2 and have a point of inflection at -3. Please try it yourself