Click on the links below for further reading on each topic:
The Binomial Theorem
Partial Fractions
There is a good video link below to help with the algebraic long division. I hope that it may clear up some puzzlement about the power order etc.
Matrices:
A link to a nice visual proof of Rotational Matrices https://www.youtube.com/watch?v=8XRvpDhTJpw
And one for the reflection in a line https://www.youtube.com/watch?v=rZiLrZjxZwE