F(x) is a function with x as the independent variable, such as y=x, or it can be written as f(x)=x, which means the same thing. F(a)=0 means that in this function f(x), when x=a, the function value is 0.

The factorial theorem is to find A that satisfies the condition of f(a)=0, and this finding process can be calculated orally. Then there is the factor x-a (because when x=a, f(a)=0, that is, when x-a=0, f(a)=0), and a factor is determined to be x-a, then the problem can be solved by comprehensive division or rational division. (Comprehensive division is relatively easy, but it can't be explained clearly in one or two sentences. Need a paper-and-pencil demonstration, so I won't elaborate here. I suggest you ask the teacher. )

The root method is to find the root of the formula through discriminant. Suppose the roots are a, b, c ... then the original formula can be written as (X-A) (X-B) (X-C). ...

Give a very simple example: x 3+2x 2 -3x, equation x 3+2x 2-3x = 0, -3 and 1, then the original formula =x(x+3)(x- 1). This is the root-seeking method. The purpose is to find the root of the equation when the original formula =0.

The factorial theorem (comprehensive division) cannot be explained clearly by computer typing.