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Updated on: 08 Nov 2023, 07:49
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.
Last edited by Bunuel on 08 Nov 2023, 07:49, edited 6 times in total.
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:33) correct
18%
(02:01)
wrong
based on 962
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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
PS07007
A. -1
B. 1
C. x
D. 1 - x
E. x - 1
PS07007
06 Jun 2014, 03:43
Kudos
Bookmarks
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
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
17 Jan 2019, 00:12
Kudos
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rashedBhai
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.
