Hi,

I have managed to factorise . But can't factorise . Can anyone help me out? Thanks

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- Dec 24th 2009, 03:58 PMM.RFactorisation
Hi,

I have managed to factorise . But can't factorise . Can anyone help me out? Thanks - Dec 24th 2009, 04:00 PMAnonymitySquared
- Dec 24th 2009, 04:09 PMBacterius
Since any expression with is always positive, then will always be positive. Thus, there is no possible factorization of such expressions in . However, there is a factorization in , which involves complex numbers.

- Dec 24th 2009, 04:27 PMM.R
I haven't done. We just started the maths course. In Chapter 1 we have so far done:

1A - Terms, Factors and indices

1B - Expanding Brackets

1C - Factorisation

1D - Algebraic Factions

1E - Four Cubic Identities. And this is where we are up to.

The answer for is given as .

So i dont' think they used complex numbers. I have tired expanding out the answer and it is correct. But i can't figure it out, how to get there? - Dec 24th 2009, 05:07 PMBacterius
No, it is wrong. You cannot obtain a

**full**factorization of in .

__Here is an example__: someone asks you to find the solutions of . You would apply your factorization to this problem, so it becomes :

Thus we are left with :

and

Oops ! None of these quadratic equations admit roots in . Now you*are*screwed without complex numbers. (Worried)

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I rather think the factorization they come up with is a bit useless, since any use you would eventually make of this factorization would anyway require complex numbers to be successfully accomplished. - Dec 24th 2009, 05:52 PMM.R
Hi Bacterius,

The question is from Cambridge Mathematics 3 Unit (year 11). Exercise 1E, question 10.

Furthermore, similar answer are given from question 11. Please have a look at http://www.mathhelpforum.com/math-he...orisation.html

So i don't know how else to figure it out with basic maths. Mind you it is from the extension question section - Dec 24th 2009, 05:55 PMBacterius
I know what you mean.

The factorization you are given is correct, but you will need to learn complex numbers to effectively use it to solve problems (furthermore, you will learn a much simpler factorization involving complex numbers when you will have learnt the later). - Dec 24th 2009, 07:24 PMM.R
Yes, your right. I am still a bit far from complex number. I think it's covered in the 4 unit (extension 2) course. But thanks again for you help

- Dec 24th 2009, 08:09 PMM.R
Thanks to Soroban, from post (http://www.mathhelpforum.com/math-he...orisation.html) i have figured it out:

[Difference of squares]