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Math Help - Are both answers right?

  1. #1
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    Are both answers right?

    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.
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  2. #2
    Senior Member eumyang's Avatar
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    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.
    Last edited by eumyang; July 16th 2010 at 03:05 PM.
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  3. #3
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    Gotcha. Thank you very much. That clears things up for me.
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  4. #4
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    Quote Originally Posted by Ingersoll View Post
    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.
    They are not really "answers".

    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.
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