In that case, I would say that " " is also not "factored completely"! The "complete" factoring would be .
Of course that's is specifically "factoring with integer coefficients". Without that restriction, we could also factor as .
Or as
There are, in fact, an infinite number of ways to factor that. Unfortunately, this text box is not large enough for me to show all of them!
Hello, allyourbass2212!
It seems there are times where its possible to arrive at different factoring results.
. . This is not true.
By definition, "factor" always means "factor completely".
Otherwise, we might have this disagreement.
Problem: factor 30.
And you could argue (forever) over who is right.
Actually:
. . and none of you factored 30 completely.
To avoid confusing the OP, we should point out that in the context of THIS question, the book appears to be asking to factorise this particular expression COMPLETELY OVER THE RATIONALS.
The highest rational common factor of and is , that is why it has been taken out.
Notice that in your solution, there is still a rational common factor of 2 inside your brackets...