Question

How do you divide `(2x ^ { 2} - 5x - 4) -: ( x - 3)`?

Answer 1

quotient `= 2x + 1`
remainder `= 1`

Explanation:

First you divide `2x^2` by `x` and get `= 2x`.

`2x` multiplied by `x - 3` is `=2x^2-6x`

`frac{2x^2 - 5x + 4}{x - 3} = 2x + frac{2x^2 - 5x + 4 - (2x^2 - 6x)}{x - 3}`

The remainder is `x + 4`, which divided by `x + 3` gives `1` and remainder `1` too.

`frac{2x^2 - 5x + 4}{x - 3} = 2x + 1 + frac{1}{x - 3}`

You could also use Briot Ruffini.