Question

How do you divide `(5x^4-3x^3+2x^2-1)div(x^2+4)` using long division?

Answer 1

The answer is `=(5x^2-3x-18)+(12x+71)/(x^2+4)`

Explanation:

Let's do the long division

`color(white)(aaaa)` `5x^4-3x^3+2x^2-1` `color(white)(aaaaaaaa)` `|` `x^2+4`

`color(white)(aaaa)` `5x^4` `color(white)(aa aaaa)` `+20x^2` `color(white)(aaaaaaaaaaa)` `|` `5x^2-3x-18`

`color(white)(aaaa)` `0-3x^3` `color(white)(aa a)` `-18x^2` `color(white)(aaaaaaa)`

`color(white)(aaaaaa)` `-3x^3` `color(white)(aaaa)` `-18x^2-12x-1` `color(white)(aaaaaaa)`

`color(white)(aaaaaaaa)` `0` `color(white)(aaaaa)` `-18x^2-12x` `color(white)(a)` `-72`

`color(white)(aaaaaaaaaaaaaaaaa)` `0` `color(white)(aaa)` `+12x` `color(white)(aa)` `+71`

Therefore,

`(5x^4-3x^3+2x^2-1)/(x^2+4)=5x^2-3x-18+(12x+71)/(x^2+4)`

The quotient is `=5x^2-3x-18`

The remainder is `=12x+71`