(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)
why isn't this 1/2?
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if x=-1, then (x^4 - x^3 + x^2) / (x-1)
Source: Beat The GMAT — Problem Solving |
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anshumishra
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Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
here, -x^3 = (-1)*x^3
we first need to execute the exponential operation, then multiply by (-1) --> (-1)*(-1)^3=1
Thus, (x^4 - x^3 + x^2) / (x-1) = [(-1)^4 + (-1)*(-1)^3 + (-1)^2)]/(-1-1) = (1+1+1)/(-2) = -3/2
we first need to execute the exponential operation, then multiply by (-1) --> (-1)*(-1)^3=1
Thus, (x^4 - x^3 + x^2) / (x-1) = [(-1)^4 + (-1)*(-1)^3 + (-1)^2)]/(-1-1) = (1+1+1)/(-2) = -3/2
anshumishra wrote:(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)
why isn't this 1/2?
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fskilnik@GMATH
- GMAT Instructor
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Hi there!
To avoid mistakes, it´s (in general) better to simplify the expression BEFORE substituting!
One possible way to do this (focusing on the fact that our denominator is x-1) is:
x^4-x^3+x^2 = x^3*(x-1) +x^2 , therefore this expression over (x-1) is surely equal to x^3 + x^2/(x-1)
Only now I would substitute: (-1)^3 equals -1 and x^2/(x-1) equals 1/(-2) = -1/2, therefore
-1+ (-1/2) = -1-1/2 = -3/2
Regards,
Fabio.
P.S.: the way you approach easy problems shows the strength you have to deal with harder ones... therefore (when you have the official answer) THINK about your approach even after you found the right alternative!!
To avoid mistakes, it´s (in general) better to simplify the expression BEFORE substituting!
One possible way to do this (focusing on the fact that our denominator is x-1) is:
x^4-x^3+x^2 = x^3*(x-1) +x^2 , therefore this expression over (x-1) is surely equal to x^3 + x^2/(x-1)
Only now I would substitute: (-1)^3 equals -1 and x^2/(x-1) equals 1/(-2) = -1/2, therefore
-1+ (-1/2) = -1-1/2 = -3/2
Regards,
Fabio.
P.S.: the way you approach easy problems shows the strength you have to deal with harder ones... therefore (when you have the official answer) THINK about your approach even after you found the right alternative!!
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
