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Math Help - simplify expression

  1. #1
    Member Mr Rayon's Avatar
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    Talking simplify expression

    According to my math teacher, when we factorise -15w+20, we always have to get -5(3w-4) and not the other possible alternative, e.g. 5(-3w+4).

    Just out of curiosity, why is this so?

    EDIT: Putting this into consideration, if I were to factorise -2t^2-8t, would t(-2-8) be correct?
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by Mr Rayon View Post
    According to my math teacher, when we factorise -15w+20, we always have to get -5(3w-4) and not the other possible alternative, e.g. 5(-3w+4).

    Just out of curiosity, why is this so?

    EDIT: Putting this into consideration, if I were to factorise -2t^2-8t, would t(-2-8) be correct?
    I think this is only true because he considers that "simplest form" for the sake of your grade I'd go along with it, but in reality, you can factor it however is most useful to you. Both of the examples you showed are correct, but in the first one that your instructor has endorsed, you factored out a negative one and a 5. In the second you only factored a 5. I assume the reason your instructor wanted you to do it this way is because he wanted the term with the variable to be positive, but I don't know for sure.

    For example, you could factor it in any of these ways (and infinitely more):

    -15w+20 = -\left(15w - 20\right)

    -15w+20 = 15\left(-w + \frac 43\right)

    -15w+20 = -20\left(\frac{3w}{4} -1\right)

    -15w+20 = w\left(-15 + \frac{20}w\right)

    -15w+20 = -w^2 \left(\frac{15}w -\frac{20}{w^2}\right)

    and so on.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Mr Rayon View Post
    According to my math teacher, when we factorise -15w+20, we always have to get -5(3w-4) and not the other possible alternative, e.g. 5(-3w+4).

    Just out of curiosity, why is this so?
    It is not so, they are equally acceptable though the second could be rewitten 5(4-3w). Your maths teacher may be using some particular convention that HS maths teachers have invented but it is not universal.

    EDIT: Putting this into consideration, if I were to factorise -2t^2-8t, would t(-2-8) be correct?
    -2t(t+4)

    (but again this may not meet with your teachers approval).

    RonL
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