# How to factor polynomials? find GCF of 8x^3b^2, 12ab^4

#### elektrisk

##### New member
Okay, so I do online schooling, and the instructions are quite confusing. Since there's obviously no one to ask, I went looking for online help sites and all I could find were sites that did the problem for me, and I want to actually know how to do it because semester exams are coming up. Thankfully, I finally found this Anyway, here's an example problem:

Code:
Find the greatest common factor of 8a^3b^2 and 12ab^4.
If there's a short & sweet explanation as to how to do this, I'd really appreciate knowing it.

Thanks!

#### Loren

##### Senior Member
Re: How to factor polynomials?

>>Find the greatest common factor of 8a^3b^2 and 12ab^4.

There is not a short sweet answer, but I'll give it a try. First consider the words "greatest common factor". Do you know and understand the word "factor" as a noun and as a verb? The next step is to understand "common factor(s)". Finally "greatest" or "largest" needs to be understood. Putting these all together we need to find common factors appearing in the two expressions 8a[sup:2n9ifikb]3[/sup:2n9ifikb]b[sup:2n9ifikb]2[/sup:2n9ifikb] and 12ab[sup:2n9ifikb]4[/sup:2n9ifikb]. Let's start by just considering the constants---those would be 8 and 12. What are their factors?

What are the factors of 8? They are 1, 2, 4, and 8. Do you know how to arrive at that? You need to.
What are the factors of 12? They are 1, 2, 3, 4, 6, and 12. Now. Out of these two lists what are the common factors?
The common factors are 1, 2, and 4. Of these common factors, which is the greatest? Of course, it is 4.
Therefore we can say that the greatest common factor of 8 and 12 is 4.

There are quicker and more efficient ways to arrive at this conclusion. But, using the same rationale you need to arrive at the greatest common factors of the variables. You will have one gcf involving "a" and one gcf involving "b". You already have the gcf involving the constants. Then simply put them all together as factors and you have the greatest common factor of 8a[sup:2n9ifikb]3[/sup:2n9ifikb]b[sup:2n9ifikb]2[/sup:2n9ifikb] and 12ab[sup:2n9ifikb]4[/sup:2n9ifikb].

P.S. These are monomials, not polynomials as the title of your post suggests.

Staff member

#### elektrisk

##### New member
Re: How to factor polynomials?

I know how to find the GCF and such of numbers, but not the exponents/variables.

#### stapel

##### Super Moderator
Staff member
elektrisk said:
I know how to find the GCF and such of numbers, but not the exponents/variables.
But now that you've studied a couple of lessons from the first lesson link (provided earlier), you do! :wink:

If you're not sure of the answer you've computed, please reply with a clear listing of your work and reasoning, so we can give it a "once over". Thank you!

Eliz.

#### mmm4444bot

##### Super Moderator
Staff member
elektrisk said:
I know how to find the GCF and such of numbers, but not the [powers of] variables.

Gosh. Is it much easier to find the GCF of symbolic powers than with real numbers? I think so.

If you need to find the GCF of a pair of real numbers, then you need to consider all of the prime factors involved.

But if you need to find the GCF of A^7 and A^15, then all of the factors are A. Clearly, seven factors is the greatest common number between these two powers of A.

I do not need to do any calculations to see that.

~ Mark