Need help with polynomial long division here...

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[bright sapphire]

Hello, do you have anyidea as to how long division works on polynomials or none

[subtle spear]

We've done a few math problems on it, so I have a rough idea...

Currently I'm calculating the second one, and I have:
(6a3 + a2 - 29a +20) : (2a - 3) = 4a2 + a
-6a3 +1a2

       2a2 - 29a + 20

[bright sapphire]

Alright so can you try doing them and if your stuck at any specific point i can guide you from there it would make it quicker for you to understand

[subtle spear]

(6a3 + a2 - 29a +20) : (2a - 3) = 4a2 + a
-6a3 +1a2

       2a2 - 29a + 20
       -2a + 3a   + 20
       --------------
                 32a + 20

[bright sapphire]

3a^2 not 4a^2

[subtle spear]

Ah...

[bright sapphire]

also there should s a +9a^2 in first line instead of just a^2

[subtle spear]

Why nine?

I mean the first line is how I got the problem by the teacher.

[bright sapphire]

3*3a2 = 9a2

let me write it break it down for you in steps give me like a few mins

look here the first thing you do is write down both the polynomials

Then check what do you need to multiply into the divisor to match the highest degree in dividend along with coefficient

the multiply the all the following numbers if any in the divisor with the same number

Then we multiply what we get from this multiplication with a -ve sign

so be careful if there is a -ve in the dividend then you put a -ve in your quotient

@subtle spear is it clear now?

[subtle spear]

Nope, I finished the equation and got like = 3a^2 + a - 13 with a -19 leftover. Frick my life.

[bright sapphire]

you know what let me make a small guide for you

[subtle spear]

I think I got somewhere.

[bright sapphire]

last term should be a -7 without a

[subtle spear]

Is the rest okay?

[bright sapphire]

yes at you will get a -1

20 -21 =-1

[subtle spear]

I don't understand how you get a -1.

At the end.

Doesn't the minus turn into a plus in the second to last line?

[bright sapphire]

@subtle spear

[subtle spear]

What about the first one?

Because I am very confused about that one.

[bright sapphire]

apply same logic i used here i will give you the first value it shouls be 4x

[subtle spear]

Then it's just... 12x^2 in the first line, no?

[bright sapphire]

you have a +8 so multiply that with 4x as well

[subtle spear]

Yeah I messed it up in the process I think.

Here's what I've written:

[bright sapphire]

read step 3

from the page above

[bright sapphire]

The first error here is 8*4 is not 16 its 32

[subtle spear]

Ah frick.

What am I supposed to even do with 17x - 32x???

Does it just go into negative numbers then?

[bright sapphire]

yes

[subtle spear]

Or did I screw it up?

Ah 41?

[bright sapphire]

so the next number in your quotation should be a negative to compensate for it

it should be a -5

[subtle spear]

Mhm, I got -5

Hang on, I'm gonna send the progress

[bright sapphire]

Thats correct

[subtle spear]

This is what I got.

[bright sapphire]

Looks correct to me

[subtle spear]

You've the patience of Job.

Thank you so much, man.