Question

How do you long divide `(x^[4] + 3x^[3] + 28x + 15)/( x + 5)`?

Answer 1

The answer is `=(x^3-2x^2+10x-22)+125/(x+5)`

Explanation:

Let's do the long division

`color(white)(aaaa)` `x^4+3x^3` `color(white)(aaaaaaaa)` `28x+15` `color(white)(aaaa)` `|` `x+5`

`color(white)(aaaa)` `x^4+5x^3` `color(white)(aaaa)` ###color(white)(aaaaaaaaaaaaaaaa)#`|` `x^3-2x^2+10x-22`

`color(white)(aaaaa)` `0-2x^3`

`color(white)(aaaaaaa)` `-2x^3-10x^2`

`color(white)(aaaaaaaaa)` `-0+10x^2+28x`

`color(white)(aaaaaaaaaaaaa)` `+10x^2+50x`

`color(white)(aaaaaaaaaaaaaaaa)` `+0-22x+15`

`color(white)(aaaaaaaaaaaaaaaaaaaa)` `-22x-110`

`color(white)(aaaaaaaaaaaaaaaaaaaaaa)` `+0+125`

Therefore,

`(x^4+3x^3+28x+15)/(x+5)=(x^3-2x^2+10x-22)+125/(x+5)`