9x^3+6x^2=0, please help!

G

Gew

New member
Joined
Aug 29, 2020
Messages
2
Hi guys!

I know this is far from rocket science, but I'm a bit retarded and my study book lacks the "Layman's terms" step-by-step guidelines for this type of equations (which usually helps me grasp), and googling the thing returns one complicated one-step-solution with lots of parenthesis and stuff after another. So please, could someone try and make me understand in really simple terms? I think I have completed the first step..

9x^3+6x^2=0 = 3x(3x^2+2x)

This is correct, is it?
Am I even supposed to start by doing this?
I can't jump straight to the "zero-product property" method, correct?
 
Someone else suggested that starting by turning the equation into ...

x(9x^2 + 6x) = 0

.. is better practice than my fumbling ..

3x(3x^2+2x)

... but I'm really clueless here! ?
 
Gew said:
Someone else suggested that starting by turning the equation into ...

x(9x^2 + 6x) = 0

.. is better practice than my fumbling ..

3x(3x^2+2x)

... but I'm really clueless here! ?
Click to expand...
You can certainly do it from there. But notice you can also factor out an extra x from what you did:
[math]9x^3 + 6x^2 = 0[/math]
[math](3x^2)(3x + 2) = 0[/math]
So either [math]3x^2 = 0[/math] or [math]3x + 2 = 0[/math]
etc.

-Dan
 
9x^3 + 6x^2 = 3*3*x*x*x + 3*2*x*x

What is common in 3*3*x*x*x and 3*2*x*x. The answer is obviously (since it is just a visual question) 3*x*x = 3x^2. So you factor out 3x^2 from 3*3*x*x*x + 3*2*x*x

What is common I put in bold. Write down what is in common and then between parenthesis write down what is in red.

This gives you 9x^3 + 6x^2 = 3x^2(3x+2) =0. When a product equals 0 one or more of the factors must = 0

Is there a value for x that makes 3=0?
Is there a value for x that makes x^2=0?
Is there a value for x that makes 3x+2=0?
 
  • Like
Reactions: Gew
topsquark said:
You can certainly do it from there. But notice you can also factor out an extra x from what you did:
[math]9x^3 + 6x^2 = 0[/math]
[math](3x^2)(3x + 2) = 0[/math]
So either [math]3x^2 = 0[/math] or [math]3x + 2 = 0[/math]
etc.

-Dan
Click to expand...
Just out of curiosity why do so many people (qualified people) always think that (in this example) that 3 is not a factor? This is not just about you Dan. I just want to know why?
 
  • Like
Reactions: Gew
Jomo said:
Just out of curiosity why do so many people (qualified people) always think that (in this example) that 3 is not a factor? This is not just about you Dan. I just want to know why?
Click to expand...
Who said that 3 is not a factor??

Not saying that 3 is a factor is very different from saying that 3 is not a factor, if that is what you are thinking.
 
Dr.Peterson said:
Who said that 3 is not a factor??

Not saying that 3 is a factor is very different from saying that 3 is not a factor, if that is what you are thinking.
Click to expand...
In my opinion when someone writes 3x^2=0 they are not thinking of 3x^2 as the product of two factors, namely 3 and x^2. If a product of factors equal 0, I feel that you should set each factor to 0 and solve. Especially when many students claim that 3=0 when x is -3
 
Otis said:
I don't understand what you're talking about.


Why would anybody need to ask themselves whether there's any situation in which the number 3 equals 0?

:confused:
Click to expand...
Integers a modulo 3?

I have no idea why you would want to otherwise.

-Dan
 
Jomo said:
In my opinion when someone writes 3x^2=0 they are not thinking of 3x^2 as the product of two factors, namely 3 and x^2. If a product of factors equal 0, I feel that you should set each factor to 0 and solve. Especially when many students claim that 3=0 when x is -3
Click to expand...
They might be thinking that way. But there's no evidence that anyone here did, and you can't read minds any better than I can.

And in saying "3x^2 [is] the product of two factors, namely 3 and x^2", are you denying that x is a factor? Of course not.

Yes, your way of saying it (which I sometimes do, too, when I first introduce the topic) is a way to emphasize that we are applying the "zero-factor theorem". However, I do that not because students don't see 3 as a factor, but because a few do, and get confused, thinking that 3 = 0 means x = 3. So I'm preemptively keeping them from going too far in that direction, and then tell them that they can ignore constant factors.

So a student should quickly move on from there and realize that they can just write 3x^2=0 and know that x = 0. So in teaching, go ahead and say what you did; but don't imply that it's wrong to say it in other ways.

One of the benefits of a forum like this is that different helpers may diagnose a student's problem in different ways, and something I don't think of, that you do, may be just what they need. Or it may not. In any case, it's not something to argue over. We're here to join forces in helping students, not to quibble over different styles.
 
I'm finding it hard to believe that students would consider 0=3 as true. How can that happen?!

?
 
You must log in or register to reply here.
Top