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Quick factoring question..please help!!

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by mustbeatgmat » Tue Oct 05, 2010 4:16 pm
Hey guys,

I have a quick question about factoring and it doesnt seem to click with me in this particular circumstance. When given x^2-5x=0, i know to factor it --> x(x-5).

HOWEVER, when trying to factor out x^3-3x=0 --> it says to factor it out like this: x^2(x-3) BUT doesnt the x^2 get distributed to the 3 too and become 3x^2 instead of just 3x?

Not sure why im not comprehending this particular case. Please help.

Thank you!
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by diebeatsthegmat » Tue Oct 05, 2010 4:40 pm
mustbeatgmat wrote:Hey guys,

I have a quick question about factoring and it doesnt seem to click with me in this particular circumstance. When given x^2-5x=0, i know to factor it --> x(x-5).

HOWEVER, when trying to factor out x^3-3x=0 --> it says to factor it out like this: x^2(x-3) BUT doesnt the x^2 get distributed to the 3 too and become 3x^2 instead of just 3x?

Not sure why im not comprehending this particular case. Please help.

Thank you!
you should post the whole question /PS... i dont understand what you are talking about
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by mustbeatgmat » Tue Oct 05, 2010 4:55 pm
sorry for the confusion! just basically wanted to know how to factor out X^3-3x=0
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by Ian Stewart » Wed Oct 06, 2010 11:10 am
mustbeatgmat wrote:Hey guys,

I have a quick question about factoring and it doesnt seem to click with me in this particular circumstance. When given x^2-5x=0, i know to factor it --> x(x-5).

HOWEVER, when trying to factor out x^3-3x=0 --> it says to factor it out like this: x^2(x-3) BUT doesnt the x^2 get distributed to the 3 too and become 3x^2 instead of just 3x?
There must be a typo in the material you're working from, or you've mistranscribed the example. If you have x^3 - 3x, you cannot factor out x^2 (at least not without getting a fraction in the brackets). You can only factor out a single x:

x^3 - 3x = x(x^2 - 3)

If you needed to, you could factor further; the expression in brackets is a 'difference of squares'. That is, we can factor it using the familiar pattern a^2 - b^2 = (a+b)(a-b). So factoring completely:

x^3 - 3x = x(x^2 - 3) = (x)(x + sqrt(3))(x - sqrt(3))
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by mustbeatgmat » Wed Oct 06, 2010 12:29 pm
Thank you!!!
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