How Can I Solve This Division Problem?

[Miike012]

Homework Statement

I added an attachment... I am not understanding how they did this...

 

[CompuChip]

Do you remember how to do long division with numbers?
For example, 6 / 5?

 

[Miike012]

no that's hard.

 

[CompuChip]

Let me give you a couple of hints...
Suppose we want to divide 63 by 5:

5) 63 (

So we check how often 5 fits in 6. Clearly, that is once, so we write 1 x 5 below the 6 and subtract it, putting the 1 on the right:

5)63 (1
   5
   ---
   1

Now we pull down the 3, and repeat the trick:

5)63 (1
   5.
   -.
   13

5 fits in 13 two times, so we get:

5)63 (12
   5
   ---
   13
   10
   ---
     3

Indeed, 63 / 5 equals 12 (because 5 x 12 = 60) and then something. But suppose we want to find some more digits, for example the first decimal. We cannot take another 5 out of 3, so we add a zero:

5) 63. (12
   5 .
   --.
   13.
   10.
   --.
    30

Now we can take out 5, and we can take it out six times:

5) 63. (12.6
   5 .
   --.
   13.
   10.
   --.
    30
    30
    ---
     0

and we have nothing left, so 12.6 is the answer.

In your example, it is the same. If you want to take 1 + 3x² out of 2x, you can do so 2x times, and since 2x(1 + 3x²) = 2x + 6x³,

1 + 3x²) 2x         ( 2x
         2x + 6x³
        ---------
            - 6x³

Next, you can take it out 6x³ times, write that underneath, and subtract.
In principle you can keep on doing this as long as you want, but in your example they stop at some point, they just take what is left and write it at the end (in the numeric example, you could stop after

5)63 (12
   5
   ---
   13
   10
   ---
     3

and just say "I don't feel like keeping on doing this, so I'll just take the remainder and divide it by 5, which gives 12 + 3/5".

 

[Miike012]

I was kidding, thank you though.

 

[CompuChip]

In that case, thanks for having me type it all out :P
You'd be surprised how many people are completely confused as soon as the words "long division" are said.

 

[Miike012]

I'm sorry, i didnt thinnk you would type it all thge way out lol. But I do still appreciate your help.