Australian Factoring

Today, our math teacher very quickly factored a quadratic equation using a method called Australian Factoring. In any case, it was nice and quick, and many people were confused, so I decided I’d give it a try and show everyone along the way.

Edit: We got confirmation that this is indeed called ‘The Australian Method’

Here is our original equation:


As usual, we will need to find 2 numbers that add up to B and multiply to AC. These numbers are:

15, -4

Now, what we do is set up something that looks like this:


Basically, we created a rational with 2 brackets on top. In each bracket, we placed A (coefficient of x) and we also placed it under the rational. At this point, we will plug our two magic numbers into the second part of the bracket.


Now, we will factor each bracket, by taking out the highest common denominator out of each.



Since the 6 on top and the 6 on the bottom reduce, we can get rid of them.



Now we know that:

x_1= \frac{-5}{2}

x_2= \frac{2}{3}




14 Responses to “Australian Factoring”

  1. 1 nikikkkkkkkkkkkkkkkiki September 22, 2007 at 2:06 pm

    hahaha o goshaaaaaaaaaaaaa
    math suck balls
    anad did she ever say it was “australian factoring”?? i do no remeber this

  2. 2 happyatom September 22, 2007 at 2:23 pm

    You know what? I THINK she said it. However, there is a very high chance that she did not. I’m still gonna call it that! 🙂

  3. 3 kyle October 3, 2007 at 7:00 pm

    It is called the Australian method. My teacher showed us this a couple of days ago. I forgot to bring home my note though so thanks for posting how to do it. Its a lot quicker than the other way (decomposition I think?)

  4. 4 happyatom October 3, 2007 at 7:42 pm

    No prob, Kyle. Yeah, the other method is called Decomposition, and this one is a lot faster if the coefficient of the leading term isn’t 1. Besides, it’s Australian!

  5. 6 happyatom October 25, 2007 at 8:42 pm

    Some guy from the Internets.

  6. 7 Green Hornet January 19, 2011 at 6:48 pm

    It’s called the Australian Method because you put A under the equation in one of the last steps. Get it, down under? Like Austrailia?

  7. 8 tyson December 10, 2011 at 7:36 pm

    how did you get the 15 ??

  8. 9 Mrs. J January 10, 2012 at 11:25 pm

    I like this method better.
    Same as you a*c=(-60) and b=11
    (15)(-4) = -60 and 15+(-4) = 11
    15 and -4 when added together is the middle term so we will replace 11x with 15x-4x Now we have
    Now factor with groupings – split the equation into 2

    6x^2 + 15x -4x-10 =0
    Now factor out a monomial from each half
    3x(2x+5) -2(2x+5) =0
    Because both halves have a common binomial factor you can put the coefficients of the factor (2x+5) together
    (3x-2) (2x+5)=0
    Therefore x=2/3 and x=-5/2

  9. 10 childrens desks June 9, 2013 at 4:51 pm

    I’m gone to say to my little brother, that he should also go to see this website on regular basis to get updated from latest gossip.

  1. 1 D - MCAS 9 Due 3/25 | The Winchell Factor Trackback on March 24, 2008 at 1:15 pm
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