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#1 2014-02-10 00:58:26

ninjaman
Member
Registered: 2013-10-15
Posts: 41

factoring

hello

i have 6t^2 -18t +12

i got (3t^2-3)(4t+2)


i did 6 * 12 = 72

2  36
3  24
4  18
6  12
8  9

middle term is 18 = 6 + 12

i put this in a box


    3       3
6t^2  |  6    2

+12   |  +12   4


not sure if this is correct?
any help
cheers

simon:)

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#2 2014-02-10 01:52:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,459

Re: factoring

Hi;

i got (3t^2-3)(4t+2)

That is incorrect. Please try again.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-02-11 02:11:44

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,384

Re: factoring

hi ninjaman,

You've got in a muddle about where to put the pair that gives 12 and the pair that gives 6.

Look at my diagram below.

There are four ?numbers to find.  The final factorisation will be like this

So ?1 times ?2 must come to 6t^2

and ?3 times ?4 must come to 12.

There are several ways of achieving this, but find one where the two 't' terms come to -18t together.

Bob

ps.  In this example, it is also possible to factorise a 6 before you start on the quadratic.  This will make it easier to find the ?s.

And a factorisation is not complete until the numbers are factorised out too.

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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