if x=-1, then (x^4 - x^3 + x^2) / (x-1)

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Tue Nov 23, 2010 5:11 pm
Location: Beijing, China
Thanked: 1 times

if x=-1, then (x^4 - x^3 + x^2) / (x-1)

by davo45 » Sat Mar 12, 2011 6:04 am
if x=-1, then (x^4 - x^3 + x^2) / (x-1)

why isn't this 1/2?

User avatar
Legendary Member
Posts: 543
Joined: Tue Jun 15, 2010 7:01 pm
Thanked: 147 times
Followed by:3 members

by anshumishra » Sat Mar 12, 2011 6:20 am
davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)

why isn't this 1/2?
(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2
Thanks
Anshu

(Every mistake is a lesson learned )

Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Sat Mar 12, 2011 6:58 am
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
anshumishra wrote:
davo45 wrote:if x=-1, then (x^4 - x^3 + x^2) / (x-1)

why isn't this 1/2?
(x^4 - x^3 + x^2) / (x-1) = (-1)^4-(-1)^3+(-1)^2/[(-1-1)] = 1-(-1)+1/(-2) = 3/-2 = -3/2
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Sun Mar 13, 2011 5:28 am
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!!
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br