Last visit was: 26 Apr 2026, 10:55 It is currently 26 Apr 2026, 10:55
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
azelastine
User avatar
Joined: 10 Nov 2013
Last visit: 13 Aug 2017
Posts: 15
Own Kudos:
11
Given Kudos: 7
Posts: 15
Kudos: 11
Factor x^4-2x^2-8 10 Nov 2013, 14:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
how would you go about it?

the factored form of the quadratic function is supposed to be a(x-x1)(x-x2)
the factors of (-8) that equal to (-2) are (-4) and (2)...so it should be (x^2+4)*(x^2-2) but the answer says (x^2-4)*(x^2+2)
???



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 Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
azelastine
User avatar
Joined: 10 Nov 2013
Last visit: 13 Aug 2017
Posts: 15
Own Kudos:
11
Given Kudos: 7
Posts: 15
Kudos: 11
Factor x^4-2x^2-8 10 Nov 2013, 14:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
in simplifying a quadratic function, i found the following....

x(3x-2)+2(3x-2)=(x+2)*(3x-2)

i vaguely remember something like this from school... however, when i looked up distributive property, the formula was actually x*(y+z)=(xy)+(xz) and not this....

what am I missing?
avatar
mayankdharwal
avatar
Joined: 06 Apr 2012
Last visit: 12 Jul 2014
Posts: 6
Own Kudos:
1
Given Kudos: 34
Posts: 6
Kudos: 1
Factor x^4-2x^2-8 10 Nov 2013, 19:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x^4 -2x^2 -8
for solving this equationg lets assume
y = x^2
so effectively ur equation is
y^2 -2y -8
we can rewrite the equation as
y^2 -4y +2y -8
=> y(y-4) + 2(y-4)
=> (y-4) (y+2)
substituting the value of y = x^2
we get, (x^2 -4) (x^2+2)

I hope it helps....
User avatar
azelastine
User avatar
Joined: 10 Nov 2013
Last visit: 13 Aug 2017
Posts: 15
Own Kudos:
11
Given Kudos: 7
Posts: 15
Kudos: 11
Factor x^4-2x^2-8 10 Nov 2013, 20:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mayankdharwal
x^4 -2x^2 -8
for solving this equationg lets assume
y = x^2
so effectively ur equation is
y^2 -2y -8
we can rewrite the equation as
y^2 -4y +2y -8
=> y(y-4) + 2(y-4)
=> (y-4) (y+2)
substituting the value of y = x^2
we get, (x^2 -4) (x^2+2)

I hope it helps....
Show more


Yes, this makes sense. I am just left wondering why the factored form of this function does not work in this case. following that form, the answer should be (x^2+4)*(x^2-2) since the formula is a(x-x1)*(x-x2) and x1=-4, x2=2...
User avatar
dabral
User avatar
Tutor
Joined: 19 Apr 2009
Last visit: 29 Nov 2024
Posts: 557
Own Kudos:
666
Given Kudos: 19
Affiliations: GMATQuantum
Expert
Expert reply
Posts: 557
Kudos: 666
Factor x^4-2x^2-8 10 Nov 2013, 21:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@azelastine

In a general quadratic equation ax^2+bx+c=0, the product of the roots is equal to c/a, -8 in this case, and the sum of the roots equal to -b/a, which is -(-2)/1=2, in this case. That is why the roots are 4 and -2 and not -4 and 2, leading to the factorization (x^2-4)(x^2+2).
User avatar
azelastine
User avatar
Joined: 10 Nov 2013
Last visit: 13 Aug 2017
Posts: 15
Own Kudos:
11
Given Kudos: 7
Posts: 15
Kudos: 11
Factor x^4-2x^2-8 10 Nov 2013, 21:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Silly question but I am still trying to remember some basic math...

why does ((x – 3)^2 + 4)((x – 3)^2 – 2) equal

((x^2 – 6x + 9) + 4)((x^2 – 6x + 9) – 2)
User avatar
MacFauz
User avatar
Joined: 02 Jul 2012
Last visit: 19 Mar 2022
Posts: 990
Own Kudos:
3,406
Given Kudos: 116
Location: India
Concentration: Strategy
Schools: Ross '16 (D) McCombs '16 (D) Kenan-Flagler '16 (WA) Olin '16 (M$) Tepper '16 (D)
GMAT 1: 740 Q49 V42
GPA: 3.8
WE:Engineering (Energy)
Schools: Ross '16 (D) McCombs '16 (D) Kenan-Flagler '16 (WA) Olin '16 (M$) Tepper '16 (D)
GMAT 1: 740 Q49 V42
Posts: 990
Kudos: 3,406
Factor x^4-2x^2-8 10 Nov 2013, 23:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\((a+b)^2 = a^2 + b^2 + 2*a*b\)

\(Illustration: (a+b)*(a+b) = a*a + a*b + b*a + b*b = a^2 + 2*a*b + b^2\)

Similarly

\((x-3)^2 = x^2 + 3^2 - 2*3*x = x^2 - 6*x + 9\)
azelastine
Silly question but I am still trying to remember some basic math...

why does ((x – 3)^2 + 4)((x – 3)^2 – 2) equal

((x^2 – 6x + 9) + 4)((x^2 – 6x + 9) – 2)
Show more



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 Quantitative Questions 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!