Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

List All Common Factors

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: List All Common Factors

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

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Re: List All Common Factors

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: List All Common Factors

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?

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Re: List All Common Factors

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,169

Re: List All Common Factors

OK, thanks for the link.  I really like this guy's teaching style; it must be great to be in his class.

He is trying to find common factors so it is sufficient to find x, x^2, x^3 etc and not bother about 3x, 3x^2 and 3x^3.

He takes care of the number factors separately so it works.

So it all depends on what the question asks for.

If it just wants the factors then 3x etc should be in the list, but if you're after the GCF you can leave them out.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

Re: List All Common Factors

OK, thanks for the link.  I really like this guy's teaching style; it must be great to be in his class.

He is trying to find common factors so it is sufficient to find x, x^2, x^3 etc and not bother about 3x, 3x^2 and 3x^3.

He takes care of the number factors separately so it works.

So it all depends on what the question asks for.

If it just wants the factors then 3x etc should be in the list, but if you're after the GCF you can leave them out.

Bob

I agree. Professor Leonard is an amazing teacher. He wants students to understand math and not just to know enough to pass the test or the class.