Algebraic Expression Factoring

The book that I am working through does an absolutely pitiful job explaining what to do in these types of problems. I have no clue as to where to begin, if someone could please walk me through and explain why each step works it would be much appreciated, or if you have an easier method other than the book entirely.

$\displaystyle 9(14x+5)^4+6x(14x+5)-(14x+5)=[9(14x+5)^3](14x+5)+6x(14x+5)-1(14x+5)$$\displaystyle =[9(14x+5)^3+6x-1](14x+5)$

Other than this the only hint the book gives me is to "factor out each expression raised to the lowest power", but if that were the case wouldn't $\displaystyle (14x+5)^1$ be the lowest?