Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find Factors

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?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,802

Re: Find Factors

You are correct!

The factors are

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Factors

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

---

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Factors

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?

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Factors

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?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Factors

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

---

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Factors

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.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Find Factors

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?

you did the factoring right
But you didn't put things back together in *all* the possible ways
AI is many times stupid at math
But it is right-er this time
All the factors are:
1, 2, 3, 4, 6, 12, 1x, 2x, 3x, 4x, 6x, 12x, 1x^2, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Factors

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?

you did the factoring right
But you didn't put things back together in *all* the possible ways
AI is many times stupid at math
But it is right-er this time
All the factors are:
1, 2, 3, 4, 6, 12, 1x, 2x, 3x, 4x, 6x, 12x, 1x^2, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2

I checked with professor Leonard. He said my answer is correct.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 256

Re: Find Factors

All the factors are:
1, 2, 3, 4, 6, 12, 1x, 2x, 3x, 4x, 6x, 12x, 1x^2, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2

If I understood well the exercise, amnkb gave the right answer.

For example. let us assume x=5
12x^2 = 300
So, its factors are:
1, 2, 3, 4, 6, 12, 5, 10, 15, 20, 30, 60, 25, 50, 75, 100, 150, 300
-----------------   -----------------------   -----------------------------

Last edited by KerimF (2024-03-01 11:07:40)

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Factors

All the factors are:
1, 2, 3, 4, 6, 12, 1x, 2x, 3x, 4x, 6x, 12x, 1x^2, 2x^2, 3x^2, 4x^2, 6x^2, 12x^2

If I understood well the exercise, amnkb gave the right answer.

For example. let us assume x=5
12x^2 = 300
So, its factors are:
1, 2, 3, 4, 6, 12, 5, 10, 15, 20, 30, 60, 25, 50, 75, 100, 150, 300
-----------------   -----------------------   -----------------------------

Ok. Sounds good. Thanks for your input.