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nycguitarguy

Member

Registered: 2024-02-24

Posts: 491

List the Factors of 3x^3

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,168

Re: List the Factors of 3x^3

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

---

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 the Factors of 3x^3

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,168

Re: List the Factors of 3x^3

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

---

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 the Factors of 3x^3

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,168

Re: List the Factors of 3x^3

Watched it. Great vid!

But I didn't hear him say what he means by 'evenly divided'.  It's not a maths expression that I'm familiar with.

Did it come from a text book question?

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 the Factors of 3x^3

Watched it. Great vid!

But I didn't hear him say what he means by 'evenly divided'.  It's not a maths expression that I'm familiar with.

Did it come from a text book question?

Bob

Evenly divided are my words to mean there is no remainder.

For example: 3x^2 ÷ x = 3x because 3x times x = 3x^2.

Given 3x^2 and 3x, find the GCF.

The GCF IS 3x. Why?

I say 3x is the GCF because 3x^2 can be evenly divided (no remainder) by 3x.

We can divide 3x^2 by 3x but the other way around.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,168

Re: List the Factors of 3x^3

Maybe the problem here is that the word factor is being used to mean two similar but different things.

If N is a whole number then another whole number m is a factor if N/m is a whole number.

eg. 8 is a factor of 48 because 48/8 = 6

But if an algebraic expression (E) can be split into two expressions (F and G) that multiply to make E then F and G are said to be factors.

eg. 

x and (x+2) are factors of E. 

If only numbers are involved then the GCF is clear,

eg The GCF of 45 and 75 is 15

In pure mathematical terms saying that the GCF of 12x^2 and 28x^4 is 4x^2 is a questionable use of GCF because we don't even know if x is a whole number so how can we ask questions about the greatest factor.

But the Prof. goes on to use his earlier method to factorise (second definition) algebraic expressions. Nothing wrong with that; methods that work but have use dubious logic do exist in maths . I teach integration by saying have a guess based on what you know about differentiation; check if it works; and modify your guess if it doesn't.

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 the Factors of 3x^3

Maybe the problem here is that the word factor is being used to mean two similar but different things.

If N is a whole number then another whole number m is a factor if N/m is a whole number.

eg. 8 is a factor of 48 because 48/8 = 6

But if an algebraic expression (E) can be split into two expressions (F and G) that multiply to make E then F and G are said to be factors.

eg. 

x and (x+2) are factors of E. 

If only numbers are involved then the GCF is clear,

eg The GCF of 45 and 75 is 15

In pure mathematical terms saying that the GCF of 12x^2 and 28x^4 is 4x^2 is a questionable use of GCF because we don't even know if x is a whole number so how can we ask questions about the greatest factor.

But the Prof. goes on to use his earlier method to factorise (second definition) algebraic expressions. Nothing wrong with that; methods that work but have use dubious logic do exist in maths . I teach integration by saying have a guess based on what you know about differentiation; check if it works; and modify your guess if it doesn't.

Bob

The idea of GCF is basic. I don't think professor Leonard wants to go too deep mathematically in a course called Intermediate Algebra. Students in such a course are beginning algebra students.