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Math Help - factorise help

  1. #1
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    factorise help

    i'd like some help,could you please help me factorise this expression

     4x^2+2x-20
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  2. #2
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    Quote Originally Posted by johnsy123 View Post
    i'd like some help,could you please help me factorise this expression

     4x^2+2x-20
    For a polynomial of form Ax^2+Bx+C, factoring is always tougher when A is greater than 1, so this involves some guess and check and as you become more familiar you can quickly do this

    For instance I can see that 4x^2+2x-20=(2x+5)(2x-4)

    Now how I got that?

    A=4 in this case, so the options for the first numbers in the parenthesis are (2x )(2x ) or (4x )(x ) since 4's factors are 1,2,2,4

    Then 20, which has factors 1,2,4,5,10,20

    We need the factors to multiply to -20 though, so one of the numbers in the parenthesis must be negative

    so we can try (2x- )(2x+ ) or (4x- )(x+ ) or (4x+ )(x- )

    now it's just a matter of how quickly you can choose factors and multiply in your head (or on paper), if we try 1 and 20 in (2x- )(2x+ ), you can see there is no way to add to +2, same with 2 and 10, but 4 and 5 do work

    if the 5 is positive and the 4 is negative, 5*-4=-20 and 2x*5+2x*-4=+2x

    so our answer is (2x-4)(2x+5)

    luckily we tried this before going onto the possibilities of (4x- )(x+ ) or (4x+ )(x- ), that can happen though and these problems could take a few minutes to solve

    there are other ways of factoring, but I find this way quickest and most effective with enough practice
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  3. #3
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    4x^2+2x-20
    Actually, the first thing you should do first is to factor out any GCFs (greatest common factors):
    2(2x^2+x-10)
    and then go through the steps that artvandalay11 wrote above:
    2(2x + 5)(x - 2)


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  4. #4
    Member great_math's Avatar
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    Quote Originally Posted by johnsy123 View Post
    i'd like some help,could you please help me factorise this expression

     4x^2+2x-20
    For quadratic equations the roots are: x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

    now it factorizes to \left( x-\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)\right) \ and\ \left(x-\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\right)

    here a=4,b=2 and c=-20
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