Question

How do you use the remainder theorem to find the remainder for the division `(n^4-n^3-10n^2+4n+24)div(n+2)`?

Answer 1

`f(-2) = 0""`
There is no remainder and `(n+2)` is a factor of `n^4 -n^3-10n^2 +4n+24`

Explanation:

Let `f(n) =n^4 -n^3-10n^2 +4n+24`

Setting `n+2 = 0" "` gives `n=-2`

Substitute `n=-2" into " f (n)""` to find the remainder.

`f(-2) = (-2)^4 -(-2)^3-10(-2)^2 +4(-2)+24`

`f(-2) = 16+8-40-8+24 =0`

As this is 0, it means there is no remainder.

This tells us that `n+2` is a factor of `n^4 -n^3-10n^2 +4n+24` and therefore divides into it exactly without leaving a remainder.