### 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

#### 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. 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. 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. October 25, 2007 at 8:26 pm

wait who is kyle?

6. October 25, 2007 at 8:42 pm

Some guy from the Internets.

7. 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?

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

how did you get the 15 ??

9. 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

10. 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
2. 2 Macey Trackback on August 10, 2009 at 12:57 am
3. 3 link dang ky 188bet Trackback on November 15, 2016 at 5:45 am
4. 4 How To Do The Australian Method Factoring | ce Trackback on December 13, 2016 at 4:51 am

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