Unfoil Method: 180x^5+102x^4-210x^3

[Zach]

So my math problem is currently 180x^5+102x^4-210x^3

So I know the first thing to do is find the GFC, which in our case would be 3x^3

After grabbing the GCF, I return with 3x^3(60x^2+34x-70)

So now I know the answer should be something like

3x^3(x+y)(x-y)

How do I know which two numbers that multiply into 60 to use?

So the x's could be (20x, 3x) (10x, 6x) (60x, 1x) ect...

How do I know which one to use? I know how to do the rest of the problem but I always find myself seemingly having to do a verbose amount of work for this answer. I feel I simply missed something when I took this all in 9th grade.

Any assistance would be appreciated!
- Zach

 

[stapel]

In your subject line, you mention the "unfoil method". What is this? (It isn't standard terminology, so it must be something specific to your textbook.) I've heard of "FOILing", but this is multiplying of two binomials, which does not appear to relate to your post.

So my math problem is currently 180x^5+102x^4-210x^3

Well, this is an expression, anyway; lacking instructions, it isn't quite a "problem", because we don't know what to do with it.

So I know the first thing to do is find the GFC, which in our case would be 3x^3

Should we assume that you are supposed to be factoring completely?

After grabbing the GCF, I return with 3x^3(60x^2+34x-70)

So now I know the answer should be something like

3x^3(x+y)(x-y)

How do I know which two numbers that multiply into 60 to use?

First, you might want to reconsider your GCF (Greatest Common Factor), since everything inside the parentheses is even, and thus divisible by 2. Second, you might want to reconsider having "y" has a variable in your factorization of the quadratic. The factorization will be something more along the lines of (ax + b)(cx - d).

Then, to learn how to factor quadratics that have a leading coefficient of something other than 1, try here. After correcting your GCF and studying the lesson at the link, you'll want to start by finding the factors of -1,050 that are 17 units apart.

 

[Zach]

In your subject line, you mention the "unfoil method". What is this? (It isn't standard terminology, so it must be something specific to your textbook.) I've heard of "FOILing", but this is multiplying of two binomials, which does not appear to relate to your post.


Well, this is an expression, anyway; lacking instructions, it isn't quite a "problem", because we don't know what to do with it.


Should we assume that you are supposed to be factoring completely?


First, you might want to reconsider your GCF (Greatest Common Factor), since everything inside the parentheses is even, and thus divisible by 2. Second, you might want to reconsider having "y" has a variable in your factorization of the quadratic. The factorization will be something more along the lines of (ax + b)(cx - d).

Then, to learn how to factor quadratics that have a leading coefficient of something other than 1, try here. After correcting your GCF and studying the lesson at the link, you'll want to start by finding the factors of -1,050 that are 17 units apart.

I want to completely factor, so wouldn't I want to use the biggest GCF?

The unfoiling method is here

https://www.youtube.com/watch?v=bTe-HhNkR28

I am simply curious on how to know which pair to use, in his example it's x² but some are like 60² and when you split the 60 you can do it a few different ways.

Is there a better way to do what I am trying to do?

 

[Deleted member 4993]

So my math problem is currently 180x^5+102x^4-210x^3

So I know the first thing to do is find the GFC, which in our case would be 3x^3

After grabbing the GCF, I return with 3x^3(60x^2+34x-70)

So now I know the answer should be something like

3x^3(x+y)(x-y)

How do I know which two numbers that multiply into 60 to use?

So the x's could be (20x, 3x) (10x, 6x) (60x, 1x) ect...

How do I know which one to use? I know how to do the rest of the problem but I always find myself seemingly having to do a verbose amount of work for this answer. I feel I simply missed something when I took this all in 9th grade.

Any assistance would be appreciated!
- Zach

That is why the factor method is rarely used when the coefficients are large composite number. In this case you need to factor (like Stapel suggested) 1050 (not 60) and look for the factors that are 17 apart. I would start from approximately √(1050 ~ 35 and see that (35 * 30 = 1050). Those are only 5 apart. So need to go further apart. Next number would be then 25. I notice 1050 = 25 * 42 .... bingo.

However,I would not use factoring for this problem!!!

 

[stapel]

I want to completely factor, so wouldn't I want to use the biggest GCF?

Yes, which is why I suggested that you correct your work to use that "biggest GCF", rather than what you'd posted earlier.

The unfoiling method is here

https://www.youtube.com/watch?v=bTe-HhNkR28

I'm not going to plow through a video to figure out what you mean. I'll assume that you're referring to factoring, a simple method of which was provided at the link.

I am simply curious on how to know which pair to use....

Use the method provided in the lesson at the link. It took me about fifteen seconds to find the solution.

 

[Zach]

Yes, which is why I suggested that you correct your work to use that "biggest GCF", rather than what you'd posted earlier.


I'm not going to plow through a video to figure out what you mean. I'll assume that you're referring to factoring, a simple method of which was provided at the link.


Use the method provided in the lesson at the link. It took me about fifteen seconds to find the solution.

Excuse my ignorance, I was just taught this way... I will look into what you're showing me.