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If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and
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02 Mar 2021, 10:18
02 Mar 2021, 10:18
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22% (01:27) wrong based on 36 sessions
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If \(x^2 − 2x − 15 = (x + r)( x + s)\) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?
A. 8
B. 2
C. − 2
D. − 3
E. − 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 8
B. 2
C. − 2
D. − 3
E. − 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and
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02 Mar 2021, 10:23
02 Mar 2021, 10:23
1
Carcass wrote:
If \(x^2 − 2x − 15 = (x + r)( x + s)\) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?
A. 8
B. 2
C. − 2
D. − 3
E. − 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 8
B. 2
C. − 2
D. − 3
E. − 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Given: x² − 2x − 15 = (x + r)( x + s)
Factor to get: (x - 5)(x + 3) = (x + r)( x + s)
Rewrite as: (x + -5)(x + 3) = (x + r)( x + s)
So, it's possible that r = -5 and s = 3
Here, r - s = (-5) - 3
= -8
Not an answer choice
Try REVERSING the factorization:
x² − 2x − 15 = (x + r)( x + s)
Factor to get: (x + 3)(x - 5) = (x + r)( x + s)
Rewrite as: (x + 3)(x + -5) = (x + r)( x + s)
So, it's possible that r = 3 and s = -5
Here, r - s = 3 - (-5)
= 8
Answer: A
Cheers,
Brent
gmatclubot
Re: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and [#permalink]
02 Mar 2021, 10:23
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