Question

How do you long divide `6x^3 + 27x - 19x^2 - 15 div 3x -5`?

Answer 1

The answer is `2x^2-3x+4+5/(3x-5)`

Explanation:

Let's do the long division
`color(white)(aaa)` `6x^3-19x^2+27x-15` `color(white)(aaa)` `∣` `3x-5`
`color(white)(aaa)` `6x^3-10x^2` `color(white)(aaaaaaaaaaaaa)` `∣` `2x^2-3x+4`
`color(white)(aaaaa)` `0-9x^2+27x`
`color(white)(aaaaaaa)` `-9x^2+15x`
`color(white)(aaaaaaaaaaa)` `0+12x-15`
`color(white)(aaaaaaaaaaaaa)` `+12x-20`
`color(white)(aaaaaaaaaaaaaaaaa)` `0+5`

The quotient is `=(2x^2-3x+4)` and the remainder is `=5`