polynomial-long-division

[robust raven]

What do you mean correctly

How do you write down the division process correctly?

[last grove]

I've seen multiple ways of people writting it down

like this

or like this

or like this

@robust raven

[last grove]

I think i got it - i used the second form after watching a bunch of videos

Im now stuck at this (n are all natural numbers) i dont get what to do here could someone solve this

[mental crow]

,w (x^(n + 1) - 1)/(x^n - 1)

Ew

I mean it cant be perfectly divided

It'd have remainder

[last grove]

yhea but what would be the remaining

[mental crow]

$x^{n + 1} - 1 = x(x^n - 1) + (x - 1)$

[cerulean violet]

Mizere

[mental crow]

x - 1 is the remainder

[last grove]

dont you write the remainder down like x-1/(x^n-1) than

so x(x^n-1)+x-1/(x^n-1)

[last grove]

could you show me all the steps you did

[mental crow]

Oh wait

This is how i've been teached to do it

[mental crow]

Its kinda like this way

[last grove]

after subtracting it the first time you have x-1 ?

oh wait

[last grove]

you forgot the ^

^n in the bottom x-1 right

[mental crow]

No

[last grove]

huh

what do you subtract to get x-1

[mental crow]

$x^{n + 1} - 1 - x(x^n - 1) = x^{n + 1} - 1 - x^{n + 1} + x = x - 1$

[cerulean violet]

Mizere

[last grove]

where is this x from

[mental crow]

To get rid of x^(n + 1) you multiply the divider by x

If it was for example x³/x, you would multiply the divider (x) by x² in order to get rid of x³

[last grove]

oh okay, that helps thank you a lot for your help

[mental crow]

Aight