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.
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 be the lowest?
lets look....ah! that thing in red
now we want to factor it out. so we pull out the lowest power. i have 4 of those terms in the first term, and one in the second and third terms respectively. so i will pull out 1. if i take one from the first term, i am left with 3, so i put the 3rd power, if i take one from the second and third terms, i don't have any left, so i am just left with their respective coefficients. thus i get:
Honestly Im still very confused. Here lets take the example
To me it seems I should do something like this, first finding the GCF for all terms
So factor out the from all terms and you would get
However the book lists the correct answer as
EDIT: it looks like for the final step in these type of problems, in this case you distribute the 6 to get and then you just 'tac' on the GCF in this case (x+1) to get for your final answer. Is this the right approach?
You can do it if you want, but it's not something you'd be asked...
I think it comes with practice that you know when to stop.
I'd say that if x is at the power 1, then you can develop without problem. Power 2, you can too, it's not too hard and it yields 3 terms which would simplify with some constant. Power 3 becomes difficult and quite unuseful because it will yield 4 terms...
The thing is, I guess 2 terms in a factor (x+y, or x-y...etc) is reasonable. Because factoring is made for writing less terms in an expression.
Is it clear ?