Please explain how does this x+1 come in this step.

https://images.app.goo.gl/EENXvrjL5DGS8oQy5 go through it

but remember that as u add x+1, u are adding a x=-1 so after doing solution , u have to remove one solution of x...

they add it just for making the question easy.. by adding x+1 u get formula of x^5+1...

same like this

actually u have to ask about x+1 factor.. and how to come in that case bcoz if u are adding a term like x+1 then after that u have to remove one soluation of x.. best regards

just multiply (x+1) both sides

In question you have various powers of x, so you have to put it in a compact form in order to use De-Movire theorm, so they have multiplied both side by (x+1) and as result LHS red...

because x = -1 will satisfy the equation so

if it satisfies the equation then x+1 will be one root of the equation. now we will furtger devide the whole equation with it

this one..