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Factoring

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hardaway7
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Factoring [#permalink] New post   18 Jan 2009, 13:20
I am having trouble factoring problems that having something in front of the x^2

For example- how would I do this?

3x^2 - 8x -3 = 0

OG says (3x+1)(x-3)

But how do you figure that out quickly?!



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zonk
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Re: Factoring [#permalink] New post   Updated on: 18 Jan 2009, 14:40
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hardaway7 wrote:
Thanks ALD-

How did you go from: 3x(x-3) + 1(x-3)=0

to:
(3x+1)(x-3)=0

Sorry I am slow!!! I don't know what is wrong with me!


now the two components of the sum -- 3x(x-3) and 1(x-3) -- both have (x-3) in common. So you can factor out (x-3) from each term.

Originally posted by zonk on 18 Jan 2009, 14:39.
Last edited by zonk on 18 Jan 2009, 14:40, edited 1 time in total.
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buffdaddy
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:39
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hardaway7 wrote:
Thanks ALD-

How did you go from: 3x(x-3) + 1(x-3)=0

to:
(3x+1)(x-3)=0

Sorry I am slow!!! I don't know what is wrong with me!


Hi Hardaway7,

if you look at 3x(x-3) + 1(x-3),
(x-3) is common to the parts being added together. So one can factor this out.

its the same as 3ab + 1b can be written as b(3a + 1)

good luck

-buff
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ALD
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:19
hardaway7 wrote:
I am having trouble factoring problems that having something in front of the x^2

For example- how would I do this?

3x^2 - 8x -3 = 0

OG says (3x+1)(x-3)

But how do you figure that out quickly?!


this is a quadratic equation. here's how you solve it.
you have to multiply the number before x^2 and the constant. so in this eq. 3 *3=9

now you factorize 9 in such a way that when you add or substract the factors you get -8x. the factors of 9 are 1, 3 and 9.
the equation can be simplified as follows

3x^2 -9x + 1x -3=0
3x(x-3) + 1(x-3)=0
(3x+1)(x-3)=0

i hope it is clear.
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hardaway7
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:35
Thanks ALD-

How did you go from: 3x(x-3) + 1(x-3)=0

to:
(3x+1)(x-3)=0

Sorry I am slow!!! I don't know what is wrong with me!
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lumone
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:55
What are doing here, Buff? :P
Are you re-taking the GMAT like me?
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hardaway7
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:58
ahhh got it!

THANKS to both of you!
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buffdaddy
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Re: Factoring [#permalink] New post   18 Jan 2009, 14:59
lumone wrote:
What are doing here, Buff? :P
Are you re-taking the GMAT like me?


Hi Lumone,

truth be told, being a fellow martian, I was compelled to help Hardaway7.

back to the application forums!

-buff
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tusharvk
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Re: Factoring [#permalink] New post   19 Jan 2009, 11:03
hardaway7 wrote:
I am having trouble factoring problems that having something in front of the x^2

For example- how would I do this?

3x^2 - 8x -3 = 0

OG says (3x+1)(x-3)

But how do you figure that out quickly?!

a fail proof way to solve a problem of the type
ax^2+bx+c=0 is
x=-b+/-sqrt(b^2-4ac)

A simpler approach is to look at the actual values of ac and b (with the signs).
Then find two integers k1 and k2 such that k1+k2 = ac and k1k2=b.
In the present situation,
ac=-9 and b=-8. Thus, k1=-9 and k2 = 1
and we get
3x^2-9x+x-3=0 and problem solved.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Factoring [#permalink]
19 Jan 2009, 11:03
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