Okay heres the question:

Okay, so I've been trying to do this with polynomial long division and other such attempts, and I just can't figure it out. Any help would be much appreciated. Thanks in advance

Let be any polynomial function. Let:

Where:

Also, let the difference between the tangent and be denoted by , which is defined:

Lets look at one example:

For

we know that:

and that:

and also that:

Its obvious that since:

We know that is a factor of , specifically that:

Now, prove generally, for all polynomial functions , that can always be written in the form:

For some function .

In other words, prove that is always a factor of for all polynomial .