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:
Also, let the difference between the tangent and be denoted by , which is defined:
Lets look at one example:
we know 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 .