Question

How do you find the quotient and remainder when `(3x^3-2x^2+x+7)` is divided by `(x^2-2x+5)`?

Answer 1

The remainder is `=-6x-13`
The quotient is `=3x+4`

Explanation:

Let's do the long division
`color(white)(aaaa)` `3x^3-2x^2+x+7` `color(white)(aaa)` `∣` `x^2-2x+5`
`color(white)(aaaa)` `3x^3-6x^2+15x` `color(white)(aaaaa)` `∣` `3x+4`
`color(white)(aaaaaa)` `0+4x^2-14x+7`
`color(white)(aaaaaaaa)` `+4x^2-8x+20`
`color(white)(aaaaaaaaaa)` `+0-6x-13`

The remainder is `=-6x-13`
The quotient is `=3x+4`