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?
Thanks.
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.
They are not really "answers".
You have three alternative ways to write the same expression.
$\displaystyle 15x^2-25x-10$
factor the 15 and the -10 to get
$\displaystyle (5x-10)(3x+1)$
factor the 5 and -10 in the left factor to get
$\displaystyle 5(x-2)(3x+1)$
$\displaystyle 15x^2-25x-10=(5x-10)(3x+1)=5(x-2)(3x+1)$
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
$\displaystyle 15x^2=25x+10$
and you want to "solve" for x, then both sides are equal, so subtract them and the answer is zero
$\displaystyle 15x^2-25x-10=0$
It's not obvious what x is yet...
$\displaystyle (5x-10)(3x+1)=0$
Now it's much clearer what x is
$\displaystyle 5(x-2)(3x+1)=0$
Clearly x=2 is a solution since if x=2, x-2=0 and 0(anything)=0.
One final step...
$\displaystyle 5(x-2)3\left(x+\frac{1}{3}\right)=0$
Now we can see that $\displaystyle x=-\frac{1}{3}$ is also a solution.
That is the advantage to factoring.