Help with factoring

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).

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)!!

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

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

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 ?

@MathEbi: PM Roy, he'll reply!

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.

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.

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...

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).