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Factoring out

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Factoring out

by Shaikha » Tue Jan 15, 2013 6:37 am
Quantity A
Sq root [4(x^4) + 6(x^2) + 9]

Quantity B
(x^2) + 3


The answer says these two are equal.
Why are we eliminating the possibility that the factors may be negative?
i.e. -[(x^2) + 3] * -[(x^2) + 3] also equals quantity A

So, when factoring out, are we expected to eliminate the possibility that the factors may be negative integers?

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by Brent@GMATPrepNow » Tue Jan 15, 2013 6:39 am
This a GRE question (a quantitative comparison question to be precise).
This question type does not appear on the GMAT.

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by ceilidh.erickson » Tue Jan 15, 2013 12:07 pm
Brent is correct that this is a GRE question format, and not something that you'd see on the GMAT.

To your question about square roots, though...

If we're given that x^2 = 81, we know that x could equal 9 or -9. A variable taken to an even power will have 2 solutions.

However, if you're given that x = sq rt(81), then x only equals positive 9. Because a root sign indicates a number and not an operation, there is only one - positive - solution.

So in this case, when you factor Sq root [(x^4) + 6(x^2) + 9] (I think there was a typo in your original), you get sq root[(x^2 + 3)^2], which is just (x^2 + 3).
Ceilidh Erickson
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