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Question about factoring (should be simple)

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by uncbeers » Sun Aug 24, 2008 12:51 am
I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!
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Re: Question about factoring (should be simple)

by sudhir3127 » Sun Aug 24, 2008 1:16 am
uncbeers wrote:I just want to make sure I am understanding this corectly...for some reason factoring these particular scenarios gives me problems.

Anyways-stolen from the GmatPrep stuff:

3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162



Now, to make sure I am understanding these correctly, if it was say:

3^x - 3^x-2 = xxx (this number is a non-issue for me)

Would the two ways to factor become:

1. 3^x (1-(1/9)) = xxx

2. 3^x-2 ((3^2)-1) = xxx

I just want to make sure I am understanding it correctly. I guess, in the same manner, you could take 5^x-1 - 5^x-3 and turn it into:

5^x-3 ((5^2) - 1)

If I am wrong please let me know! Thank you!
Ur Absolutely right !!!
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by AlaaQasem » Sun Aug 24, 2008 7:33 am
You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)
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by Ian Stewart » Sun Aug 24, 2008 7:55 am
Yes, with that one small correction, everything looks perfect.
3^x - 3^x-1 = 162

It seems there are two ways to factor this one through:

1. 3^x (1-(1/3)) = 162

2. 3^x-1 ((3^1)-1) = 162
I'd just add one thing- you can factor 3^x - 3^x-1 in more than two ways, though most of the ways you might factor won't be helpful. You can factor it any way you like, in fact. You could factor out a 7 if you want to:

3^x - 3^(x-1) = 7[ (3^x/7) - (3^(x-1)/7)]

or you could factor out 3^2:

3^x - 3^(x-1) = (3^2)[3^(x-2) - 3^(x-3)]

The main thing is to recognize what would be most useful to factor out, and in the question

3^x - 3^(x-1) = 162

the most useful factorizations are the two that you suggest: factoring out 3^x, or probably even better, factoring out 3^(x-1).
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by uncbeers » Sun Aug 24, 2008 9:42 am
I think the 5^2 was a typo but either way thanks for confirming and correcting.

THank you to Ian as well for the additional info-all is clear and rally helps to look at it and figure that out.
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by rbansal » Mon May 09, 2011 5:39 pm
AlaaQasem wrote:You are right but for the last statement it is going to be like this instead:
5^x-3 ((5^3) - 1)

Why is it a 3 and not a 2?
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