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:

6x^2+11x-10=0

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:

\frac{(6x)(6x)}{6}=0

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.

\frac{(6x+15)(6x-4)}{6}=0

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

\frac{3(2x+5)2(3x-2)}{6}=0

\frac{6(2x+5)(3x-2)}{6}=0

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

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

Voila!

Now we know that:

x_1= \frac{-5}{2}

x_2= \frac{2}{3}

🙂

-Gosha

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14 Responses to “Australian Factoring”


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

    hahaha o goshaaaaaaaaaaaaa
    math suck balls
    bbababallls
    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.
    6x^2+11x-10=0
    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
    6x^2+15x-4x-10=0
    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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