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If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is

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NoHalfMeasures
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If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   Updated on: 08 Nov 2023, 07:49
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B
C
D
E

Difficulty:

15% (low)

Question Stats:

81% (01:31) correct 19% (01:55) wrong based on 616 sessions
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If \(x\neq{-1}\), then \(\frac{1- x^{16}}{(1+x)(1+x^2)(1+x^4)(1+x^8)}\) is equal to

A. -1
B. 1
C. x
D. 1 - x
E. x - 1

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Official Answer
D

Originally posted by NoHalfMeasures on 06 Jun 2014, 03:03.
Last edited by Bunuel on 08 Nov 2023, 07:49, edited 6 times in total.
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PareshGmat
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Re: If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   06 Jun 2014, 03:43
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Bunuel, Thanks for the correction :)

Answer = D

Numerator

\(1 - x^{16}\)

\(= (1 + x^8) (1 - x^8)\)

\(= (1 + x^8) (1 + x^4) (1 - x^4)\)

\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 - x^2)\)

\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)\)

Denominator

\((1 + x^8) (1 + x^4) (1 + x^2) (1 + x)\)


Expanded / simplified equation would be

\(\frac{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)}{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x)}\)


= 1 - x

Answer = D
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Re: If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   17 Jan 2019, 00:12
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Expert Reply
rashedBhai wrote:
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to


A. -1
B. 1
C. x
D. 1-x
E. x-1


how to pick number in this question? Bunuel


Pick x = 1. In this case the numerator is 0, thus the whole fraction is 0. Now, plug x = 1 into the options to check which of them give 0. Only D and E fit.

Now, pick x = 2. In this case the numerator is negative and the denominator is positive, thus the whole fraction is negative. Out of D and E, only D is negative if x = 2.


Answer: D.
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rashedBhai
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Re: If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   17 Jan 2019, 00:03
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to

A. -1
B. 1
C. x
D. 1-x
E. x-1


how to pick number in this question? Bunuel
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Re: If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   17 Jan 2019, 00:25
NoHalfMeasures wrote:
If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to

A. -1
B. 1
C. x
D. 1-x
E. x-1


A question in which basic formula works a^2 - b^2 = (a-b) (a+b)

Now you can expand the numerator as

1-x^16 = (1-x) (1+x) (1+x^2) (1+x^4) (1 + x^8)

Which will result in Answer D
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DanTheGMATMan
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If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink] If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is   16 May 2024, 07:35
Expert Reply
Difference of squares:

­
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If x -1, then (1 - x^16)/((1 + x)(1 + x^2)(1 + x^4)(1 + x^8)) is [#permalink]
16 May 2024, 07:35
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