1. ## Are both answers right?

Is one more right than the other? Or is A wrong simply due to method?

Thanks.

2. 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.

3. Gotcha. Thank you very much. That clears things up for me.

4. Originally Posted by Ingersoll

Is one more right than the other? Or is A wrong simply due to method?

Thanks.

You have three alternative ways to write the same expression.

$15x^2-25x-10$

factor the 15 and the -10 to get

$(5x-10)(3x+1)$

factor the 5 and -10 in the left factor to get

$5(x-2)(3x+1)$

$15x^2-25x-10=(5x-10)(3x+1)=5(x-2)(3x+1)$

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

$15x^2=25x+10$

and you want to "solve" for x, then both sides are equal, so subtract them and the answer is zero

$15x^2-25x-10=0$

It's not obvious what x is yet...

$(5x-10)(3x+1)=0$

Now it's much clearer what x is

$5(x-2)(3x+1)=0$

Clearly x=2 is a solution since if x=2, x-2=0 and 0(anything)=0.

One final step...

$5(x-2)3\left(x+\frac{1}{3}\right)=0$

Now we can see that $x=-\frac{1}{3}$ is also a solution.

That is the advantage to factoring.