Question

How do you divide `s+s^2 -8` by `x+4`?

Answer 1

`-2 + (s^2+s +2x)/(x+4)`

Another way of writing it: `-2 + (s^2+s)/(x+4) + (2x)/(x+4)`

Explanation:

I do not know how to set up long division on this site so I will do my best without it:

Based on the assumption you mean: `(s^2+s -8) div (x+4)`

There is nothing to associate `x` with `s` so the only thing we can reasonably divide are the constants of (-8) and 4. We would then be left over with some form of unsolvable fraction which would have to be written 'as is'.

Write `(s^2+s -8) div (x+4)" as "(s^2+s -8)/(x+4)`

considering just the constants: `(-8) div 4 = -2`

So the first part of our solution is -2

If the division gives -2 then we have to subtract
`-2 times (x+4) = -2x - 8` ................ ( 1 )
from the original expression to determine what is left. This in turn will also have to be divided by `( x + 4 )`. This process is like the old remainder system you would have been taught some years back.

so we have in effect a remainder of:

`( (s^2 + s -8 ) - (-2)(x+4))/(x+4)`

`( (s^2 + s -8 ) +2(x+4))/(x+4)` ....... ( 2 )

Adding the remainder to the first part we have:

`"part (1) + part(2)"-> -2 + ( (s^2 + s -8 ) +2(x+4))/(x+4)`

This would give:

`-2 + (s^2+s +2x)/(x+4)`

or `-2 + (s^2+s)/(x+4) + (2x)/(x+4)`

Addendum: Checking the solution

If my solution is correct then multiplying it by `(x+4)` should give us the original expression. This would take the form:

`(x+4)[-2+(s^2+s+2x)/(x+4)]`

`=> -2x -8 +s^2 + s +2x`

which gives us: `s^2 + s -8`
so correct!!!!