The zeros of the function are: 1 and 3
These are the x intercepts. This is where the graph crosses the horizontal x axis.
The term "root" is another term for "zero". I prefer the term "root" since the term "zero" implies that the root could be zero, but in reality the root could be any real number.
========================================
Use the roots 1 and 3 to construct the factorization
So we start with x = 1 or x = 3
Then we get everything to one side so that 0 is on the other side
x = 1 turns into x-1 = 0
x = 3 turns into x-3 = 0
So we now have x-1 = 0 or x-3 = 0. Use the zero product property to get
(x-1)(x-3) = 0
The factorization is (x-1)(x-3)