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If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)

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If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

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New post Updated on: 06 Jun 2014, 02:34
3
8
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:28) correct 23% (02:18) wrong based on 186 sessions

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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

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Originally posted by NoHalfMeasures on 06 Jun 2014, 02:03.
Last edited by NoHalfMeasures on 06 Jun 2014, 02:34, edited 4 times in total.
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Re: If x#0, 1- x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

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New post 06 Jun 2014, 02:43
6
3
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#0, 1- x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

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New post 06 Jun 2014, 02:28
1
Is this the value we require to find? Kindly confirm


\(1 - \frac{x^{16}}{(1+x)(1+x^2)(1+x^4)(1+x^8)}\)
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Re: if x#0, 1- x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)  [#permalink]

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New post 06 Jun 2014, 02:31
1
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Re: if x#0, 1- x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8) &nbs [#permalink] 06 Jun 2014, 02:31
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