Factorisation

garfield · **Posted:** Sat, 14 Jan 2012 04:35:05 UTC

Hello everybody,

I'm just not sure how to go about factorising this one...I'm sure i've done these before but I cannot remeber how...

Any hints or pointers would be much appreciated.

Denis · **Posted:** Sat, 14 Jan 2012 04:49:50 UTC

gareth wrote:

Drop the y's (makes it easier): 3x^2 - 10x + 8
factor: (3x - 4)(x - 2) ; use quadratic formula if necessary
put y's back in: (3x - 4y)(x - 2y)

NOTE: dropping the y's is just a suggestion...no need to do what I do!

garfield · **Posted:** Sat, 14 Jan 2012 06:28:05 UTC

OK, thanks heaps - I didn't realise that it was that easy...I thought there was some other process a little more mathematical!!!! :wink:

Shadow · **Posted:** Sat, 14 Jan 2012 10:22:28 UTC

gareth wrote:

OK, thanks heaps - I didn't realise that it was that easy...I thought there was some other process a little more mathematical!!!! :wink:

Denis' method is quite mathematical, consider this version of what you're doing:

$y^2(3({x\over y})^2-10{x\over y}+8)$ . Now let $z={x\over y}$ . Then Denis' factoring is the same as doing this, only his "drop the ys then do it with x" is secretly this factorization, and hiding the substitution of a single variable for the expression ${x\over y}$ which is essentially him overloading the x. Then the whole "putting the ys back in" is exactly multiplying back through and using yz=x.

garfield · **Posted:** Mon, 16 Jan 2012 01:28:42 UTC

Oh, I get it now.....Thanks a lot!!!

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Factorisation

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