BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Help with factoring

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Jun 19, 2011 11:08 pm

Help with factoring

by MathEbi » Sun Jun 19, 2011 11:15 pm
Please read my 2nd post 1st, as it contains the actual problem

I think I've really missed something important when it comes to factoring. I learned FOIL and the other way around, but often times I see practice questions that ask for factoring and those methods don't seem to relate. For example:


Simplify:
6ab(2b^2-a) / 3ab

It says the answer is 2(2b^2-a), and tells me that I should first factor out common terms in the numerator.

What does this mean? Is there some 'factoring' technique that I missed? If you have any information on how to do this and other factoring problems, I'd really really appreciate it. I looked on this site and found a guide that didn't seem to explain what I was looking for.[/b]
Last edited by MathEbi on Mon Jun 20, 2011 1:09 am, edited 1 time in total.
Top
Source: — Problem Solving |
GMAT Instructor
Posts: 19
Joined: Mon Feb 21, 2011 7:28 am
Thanked: 6 times
Followed by:3 members

by Roy@MasterGmat » Mon Jun 20, 2011 12:23 am
Simplify:
6ab(2b^2-a) / 3ab
Simplifying this fraction demands only reducing 3ab; there aren't any additional common factors to extract. Is this the original expression, or the expression following extracting the common factor? Can you supply another example of the process you're asking about?

As for the simplified result of the fraction you've supplied, reducing 3ab results in 2 in the numerator (since 6ab:3ab = 2), hence the result is 2(2b^2-a).
Roy
Master GMAT
Top
Master | Next Rank: 500 Posts
Posts: 370
Joined: Sat Jun 11, 2011 8:50 pm
Location: Arlington, MA.
Thanked: 27 times
Followed by:2 members

by winniethepooh » Mon Jun 20, 2011 12:29 am
Look, factoring is a technique you build over time.
Math as a whole is something you expertise with time.
Reading this link might provide a bit of help!

https://www.purplemath.com/modules/factnumb.htm

For the answer to your question:
What has been done to simplify is just that the denominator and numerator contain the same terms that is 6ab/3ab.
So, multiplying 3ab by 2 will give you 6ab, hence the numerator is 2(into bracket the same previous terms in the question it self)!!
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Jun 19, 2011 11:08 pm

by MathEbi » Mon Jun 20, 2011 1:07 am
Thank you very much for your replies. I understand how this was done now...actually this came as the solution to the bigger problem, which I don't understand:

Simplify:

12ab^3-6a^2b / 3ab

So it goes from there to 6ab(2b^2-a) / 3ab , which is the 2nd step.

So I guess the factoring part is going from the 1st part to the 2nd. This is in the manhattan fractions book - and I understood all the problems so far until this one. But when I took the GMAT last year (this will be my 2nd time) there were some problems similar to this and I couldn't answer them. I read winniethepooh's link but I'm not sure how it helps with this problem. It probably does, but I couldn't figure out the relation.

Anyways thanks for the help
Top
GMAT Instructor
Posts: 19
Joined: Mon Feb 21, 2011 7:28 am
Thanked: 6 times
Followed by:3 members

by Roy@MasterGmat » Mon Jun 20, 2011 2:10 am
Simplify:

12ab^3-6a^2b / 3ab

So it goes from there to 6ab(2b^2-a) / 3ab , which is the 2nd step.

Simplifying the numerator demands only extracting a common factor (simple factoring), although it's a pretty difficult instance of the procedure.

Ask yourself: which factors (variables or numbers) appear both in 12ab^3 and in 6a^2b?

This becomes easier if you treat the numbers and the variables separately.


Start with the numbers: The greatest common factor of 6 and 12 is 6 (since both are divisible by 6).


Then, proceed to the variables: for a certain variable to constitute a common factor, it must appear in both terms. Both a and b appear in both of our terms, and may therefore be extracted as a common factor. Hence, our common factor is '6ab':


6ab*( )


Fill the brackets with the factors remaining in each of the terms after extracting 6ab. (ask yourself: by what do we need to multiply 6ab to reach each of the two terms?)

6ab*(2b^2 - a)


I'll sum this up with two additional examples:

1. 3x^2y + 9y^2x = 3xy(x+3y)

2. 12x^3y^2 + 9xy^2 = 3xy^2(4x^2 + 3)


Work out why these are correct, and you're good to go ;)
Last edited by Roy@MasterGmat on Mon Jun 20, 2011 11:22 pm, edited 1 time in total.
Roy
Master GMAT
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Jun 19, 2011 11:08 pm

by MathEbi » Mon Jun 20, 2011 4:22 pm
Wow, thank you so much, Roy! Thanks to your explanation, now I understand these. Now I just need extra practice. Does anyone know where I can find other questions of this type? Is there a special name for them?

Also, for your 3rd problem, is the answer 3xy^2(4x^2+3) ? So you can multiply 3*4=12 ?
Top
Master | Next Rank: 500 Posts
Posts: 370
Joined: Sat Jun 11, 2011 8:50 pm
Location: Arlington, MA.
Thanked: 27 times
Followed by:2 members

by winniethepooh » Mon Jun 20, 2011 7:48 pm
@MathEbi: PM Roy, he'll reply!
Top
GMAT Instructor
Posts: 19
Joined: Mon Feb 21, 2011 7:28 am
Thanked: 6 times
Followed by:3 members

by Roy@MasterGmat » Mon Jun 20, 2011 11:21 pm
Most welcome! I'm glad I could help.

Also, for your 3rd problem, is the answer 3xy^2(4x^2+3) ? So you can multiply 3*4=12 ?
Yea, it is. Little typo there, sorry about that. I corrected the post.
Roy
Master GMAT
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Sun Jun 19, 2011 11:08 pm

by MathEbi » Fri Jun 24, 2011 6:23 am
I PM'd Roy but I guess he's busy. Does anyone have a link to some extra problems in this general area? I get the feeling that factoring is a useful GMAT skill, so I want to figure out how to apply it to my repertoire.
Top
User avatar
Newbie | Next Rank: 10 Posts
Posts: 3
Joined: Tue Oct 18, 2011 9:59 am

by silverwolf » Wed Nov 09, 2011 6:18 am
Another problem:

2x^4 + 14x^2 + 24

What is the procedure for factoring this? The answer should be: 2(x^2+3)(x^2+4) but I don't know how to get there...
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Wed Nov 09, 2011 7:20 am
silverwolf wrote:Another problem:

2x^4 + 14x^2 + 24

What is the procedure for factoring this? The answer should be: 2(x^2+3)(x^2+4) but I don't know how to get there...
Given expression:
2x^4 + 14x^2 + 24

Factor out 2:
= 2(x� + 7x² + 12)

To continue, we need two integers whose sum is 7 (3+4=7) and whose product is 12 (3*4=12):
= 2(x² + 3)(x² + 4).
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1