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06 Jul 2017, 19:37
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B
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50% (01:23) correct
50%
(02:33)
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If x^5-5x^3+4x is the product of consecutive positive integers, what is the range of the sequence?
A. 3
B. 4
C. 5
D. 6
E. 7
source:self
A. 3
B. 4
C. 5
D. 6
E. 7
source:self
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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06 Jul 2017, 19:47
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gracie
If x^5-5x^3+4x is the product of consecutive positive integers, what is the range of the sequence?
A. 3
B. 4
C. 5
D. 6
E. 7
source:self
A. 3
B. 4
C. 5
D. 6
E. 7
source:self
Let the integers be \(y-2, y-1, y, y+1, y+2\)
Range = \(y + 2 - y + 2 = 4\). Ans - B.
06 Jul 2017, 19:54
Kudos
Bookmarks
x^5 - 5x^3 + 4x can be written as:
x (x^4 - 5x^2 + 4) = (take out x common)
x (x^4 - 4x^2 - x^2 + 4) = (factorising)
x {x^2(x^2-4) - 1(x^2-4)} =
x (x^2-1) (x^2-4) =
x (x-1)(x+1)(x-2)(x+2) OR (x-2)(x-1)x(x+1)(x+2)
Thus the above algebraic expression is the product of 5 consecutive integers.. Thus range = x+2 - (x-2) = 4.
Hence B answer
x (x^4 - 5x^2 + 4) = (take out x common)
x (x^4 - 4x^2 - x^2 + 4) = (factorising)
x {x^2(x^2-4) - 1(x^2-4)} =
x (x^2-1) (x^2-4) =
x (x-1)(x+1)(x-2)(x+2) OR (x-2)(x-1)x(x+1)(x+2)
Thus the above algebraic expression is the product of 5 consecutive integers.. Thus range = x+2 - (x-2) = 4.
Hence B answer
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
