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#1001 Re: Help Me ! » List All Common Factors » 2024-02-26 03:25:38

mathxyz
Bob wrote:

Let's take one of my list that isn't in yours.

eg.  3x

Is this a factor of both expressions?

6x^3/3x = 2x^2    15x^4/3x = 5x^3

In both cases the answer is yes, it is a factor.

Bob

ps. What text are you working from?

Again, professor Leonard explains this topic in his lesson 1 for Intermediate Algebra on YouTube. Perhaps, I didn't understand the lesson well.

#1002 Re: Help Me ! » List the Factors of 3x^3 » 2024-02-26 03:23:37

mathxyz
Bob wrote:

I don't understand how it can mean that for this question, because that's what is required for a factor. My list is for all the factors.  The question wants less but I don't know what ones to leave out.

Bob

To find out exactly what the question requires, watch professor Leonard's Intermediate Algebra lesson on YouTube.

#1003 Help Me ! » Find GCF Involving Variables » 2024-02-25 18:11:48

mathxyz
Replies: 2

Find the GCF.


a^4 b^2, a^3 b^5, a^2 b^3


What is the biggest a term that evenly divides a^4, a^3 and a^2?


I say x^2.


What is the biggest b term that evenly divides b^2, b^5, and b^3?


I say b^2.


My final answer is a^2 b^2.


You say?

#1004 Help Me ! » GCF Involving Variables » 2024-02-25 17:53:22

mathxyz
Replies: 2

For each example, find the GCF.


Sample A


-18y^2, -63y^3, 27y^4


So, the biggest number that evenly divides -18, -63 and 27 is 9.
The biggest variable term that evenly divides y^2, y^3 and y^4 is y^2.


The GCF is 9y^2.


You say?


Sample B


4x^2, x^3, 3x^6


Let me see. I say that 1 is the only coefficient in this example that evenly divides 1, 3, and 4.

With respect to the variables, x^2 evenly divides into x^2, x^3, and x^6.


The GCF is 1•x^2 or simply x^2.
You say?

#1005 Re: Help Me ! » List All Common Factors » 2024-02-25 14:09:51

mathxyz
Bob wrote:

List all common factors of 6x^3 and 15x^4.

I think: { 1, 3, 1x, 3x, 1x^2, 3x^2, 1x^3, 3x^3}

Bob

Bob,

The factors common with respect to both terms are
1, 3, x, x^2, x^3. Those are the factors found on the list for both terms.
Yes? No?

#1006 Re: Help Me ! » GCF of 32 and 33 » 2024-02-25 14:05:18

mathxyz
Bob wrote:

GCF is 1 tick.

Relatively prime tick apparently. I'd not met this term but Wolfram Alpha agrees so it must be true..

Bob

Ok. That works for me. Questions will get increasingly harder as I go through the chapters in.my self-study of algebra 1 and 2 topics.

#1007 Re: Help Me ! » Find GCF » 2024-02-25 14:03:33

mathxyz
Bob wrote:

I'm happy with your working and final answer.   smile

Bob

Thank you, Bob. I try showing my work when time allows.

#1008 Re: Help Me ! » List the Factors of 3x^3 » 2024-02-25 13:58:15

mathxyz
Bob wrote:

List the factors of 3x^3.

Note: Do not consider factors that are evenly divided by 3x^3. For example, 3x should not be on your list.

I have no idea what 'evenly divided' means in this question so I'll list them all.

I think {1, 3, 1x, 3x, 1x^2, 3x^2, 1x^3, 3x^3}

The underlined 1s could be omitted.

Bob

I guess [evenly divided] means to divide one term by another without a remainder. Is my work correct? If not, why not?

#1009 Help Me ! » GCF of 32 and 33 » 2024-02-25 02:53:38

mathxyz
Replies: 2

Find the GCF of 32 and 33.


Last one for today.


Factors of 32: 1, 2, 4, 8, 16, 32.


Factors of 33: 1, 3, 11, 33.


I say the GCF is 1.


I saw online that when two numbers have no GCF except for 1 it is called RELATIVELY PRIME. Is this correct?


Thanks....

#1010 Help Me ! » Find GCF » 2024-02-25 02:47:05

mathxyz
Replies: 4

Find the GCF of 45 and 75.


I will start by listing the factors of each.


Factors of 45: 1, 3, 5, 9, 15, 45


Factors of 75: 1, 3, 5, 15, 25, 75


The common factors are 1, 3, 5, and 15.


Which is the biggest? The biggest is 15.


So, the GCF of 45 and 74 is 15.


You say?

#1011 Help Me ! » List All Common Factors » 2024-02-25 02:32:09

mathxyz
Replies: 6

List all common factors of 6x^3 and 15x^4.


Just having fun with this stuff.


Factors of 6: 1, 2, 3, 6.


Factors of x^3: x, x^2, x^3.


Factors of 6x^3: 1, 2, 3, 6, x, x^2, x^3.


Do the same for 15x^4.


Factors of 15: 1, 3, 5, 15.


Factors of x^4: x, x^2, x^3, x^4.


Factors of 15x^4: 1, 3, 5, 15, x, x^2, x^3, x^4.


List the common factors of 6x^3 & 15x^4.


Here they are: 1, 3, x, x^2, x^3. 


What do you say?

#1012 Help Me ! » List the Factors of 3x^3 » 2024-02-25 02:24:51

mathxyz
Replies: 8

List the factors of 3x^3.

Note: Do not consider factors that are evenly divided by 3x^3. For example, 3x should not be on your list.

Let me see what I can do here.

Factors of 3: 1, 3.

Factors of x^3: LIST VARIABLES WHOSE EXPONENTS ARE UNDER x^3 including x^3. So, the factors are x, x^2, x^3.

My final answer is 1, 3, x, x^2, x^3

Yes? No?

#1013 Re: Help Me ! » Find Common Factors » 2024-02-25 02:05:26

mathxyz
Jai Ganesh wrote:
FelizNYC wrote:
Bob wrote:

1 is also a common factor.

Bob

Bob,

The number 1 does not appear multiple times. I listed all the factors of 12x^2 and x^4. The number 1 appears on the list for factors of 12 only. You say?

When counting the factors, it goes without saying 1 is a factor; it is obvious. For example, in perfect numbers, the first perfect numbers are 6, 28, ...

When we talk of factors, one and the number itself are excluded, by convention.

1. What do you mean by perfect number?

2. You said: . . ."one and the number itself are excluded, by convention." What do you mean by this statement?

#1014 Re: Help Me ! » Find Common Factors » 2024-02-25 02:02:21

mathxyz
Bob wrote:

The factors of x^2 are {1, x, x^2}

The factors of x^4 are {1, x, x^2, x^3, x^4}

1 is always a factor of anything because it always divides exactly. So it is always a common factor.

Bob

Ok. I will post more later.

#1015 Re: Help Me ! » Find Factors » 2024-02-25 00:52:12

mathxyz
Bob wrote:

I'm assuming AI questions is a 'robot'.  Robots don't always get things right because 'their' answers depend on the programming by humans.

Recommended background reading: I Robot series by Isaac Azimov.

How to test if something is a factor: Does it divide exactly?

The AI doesn't list x^2 but (12x^2)/x^2 = 12 so it is a factor.

If you write the expression like this:

then a factor can be 'constructed' by taking some of the above factors multiplying them together.

Thus: leave out all the xs and you have the usual number factors {1, 2, 3, 4, 6, 12}

Now include one x and you have {1x, 2x, 3x, 4x, 6x, 12x}

Now include both xs and you have {1x^2, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2}

I'm claiming that a systematic approach like this makes sure none are left out.

Bob


Bob,

AI Questions is an app. The app also answers word problems in great detail. Sometimes the answer is right, sometimes it is wrong and way off. I will post a few more later today.

#1016 Re: Help Me ! » Find Common Factors » 2024-02-24 20:46:09

mathxyz
FelizNYC wrote:
Bob wrote:

1 is also a common factor.

Bob

Bob,

The number 1 does not appear multiple times. I listed all the factors of 12x^2 and x^4. The number 1 appears on the list for factors of 12 only once. You say?

#1017 Re: Help Me ! » Find Common Factors » 2024-02-24 20:44:43

mathxyz
Bob wrote:

1 is also a common factor.

Bob

Bob,

The number 1 does not appear multiple times. I listed all the factors of 12x^2 and x^4. The number 1 appears on the list for factors of 12 only. You say?

#1018 Re: Help Me ! » Find Common Factors » 2024-02-24 20:42:38

mathxyz
Jai Ganesh wrote:

Hi FelizNYC,

Welcome the forum!

You are correct!

Jai

Bob also said that 1 is a common factor, too. The number 1 does not appear multiple times. Explain.

#1019 Re: Help Me ! » Find Factors » 2024-02-24 20:40:18

mathxyz
Bob wrote:

hi FelizNYC

Welcome to the forum.

I think there are more than this.

eg. 2x is a factor; 2x^2 is a factor.

If you treat x as 1x and x^2 as 1x^2 then there must be

6 factors where no x is present

6 factors where x and a number is present.

6 factors where x^2 and a number is present.

Bob

Bob,

You know, the AI Questions app tells me that the factors are
1, 2, 3, 4, 6, x, 2x, 4x, 6x. I also know that my work is correct. Who's right?

#1020 Re: Help Me ! » Find Factors » 2024-02-24 20:39:06

mathxyz
Jai Ganesh wrote:

You are correct!

The factors are

Thanks Jai. You know, the AI Questions app tells me that the factors are
1, 2, 3, 4, 6, x, 2x, 4x, 6x. I also know that my work is correct. Who's right?

#1021 Help Me ! » Find Common Factors » 2024-02-24 16:57:12

mathxyz
Replies: 9

Find the common factors of 12x^2 & x^4.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of x^2: x, x^2

Factors of x^4: x, x^2, x^3, x^4

Common factors: x, x^2

Is this correct?

#1022 Help Me ! » Find Factors » 2024-02-24 16:53:27

mathxyz
Replies: 10

Find the factors of 12x^2.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of x^2: x, x^2

My answer is 1, 2, 3, 4, 6, 12, x, x^2

You say?

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