15x^2 -25x -10. Answer A: (5x-10)(3x+1). Answer B: 5(3x+1)(x-2).
Is one more right than the other? Or is A wrong simply due to method?
Depends on what you mean by "right." If the question is to factor completely, then Answer B would be better, because in the first factor of Answer A (5x - 10), you can factor out the greatest common monomial factor, which is 5. So
(5x - 10)(3x + 1) =
5(x - 2)(3x + 1)
... which is Answer B with the binomials swapped.
You have three alternative ways to write the same expression.
factor the 15 and the -10 to get
factor the 5 and -10 in the left factor to get
If you choose any value for x, you will get the same result if you place it in any of the 3 equivalent versions of the expression.
If however, you began from
and you want to "solve" for x, then both sides are equal, so subtract them and the answer is zero
It's not obvious what x is yet...
Now it's much clearer what x is
Clearly x=2 is a solution since if x=2, x-2=0 and 0(anything)=0.
One final step...
Now we can see that is also a solution.
That is the advantage to factoring.