Question

How do you use synthetic division to divide `(3x^3 - 17x^2 + 15x - 25) -: (x-5)`?

Answer 1

`3x^2-2x+5`

Explanation:

`color(white)(aaaa)` `3x^3-17x^2=15x-25` `color(white)(aaaa)` `∣` `color(green)(x-5)`

`color(white)(aaaa)` `2x^3-15x^2` #color(white)(aaaaaaaaaaaaaa # `∣` `color(red)(3x^2-2x+5)`
`color(white)(aaaaa)` `-----`

`color(white)(aaaaaaa)` `0-2x^2+15x`

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

`color(white)(aaaaaaaaaaaaa)` `0-5x-25`

`color(white)(aaaaaaaaaaaaaaa)` `-5x-25`
`color(white)(aaaaaaaaaaaaaaa)` `-----`

`color(white)(aaaaaaaaaaaaaaaa)` `-0-0`

The remainder is `=0` and the quotient is `=3x^2-2x+5`

`(3x^3-17x^2+15x-25)/(x-5)=3x^2-2x+5`

`color(white)(aaaa)` `3x^3-17x^2+15x-25` `color(white)(aaaa)` `∣` `color(green)(x-5)`
`color(white)(aaaa)` `x-5` `color(white)(aaaaaaaaaaaaaaaaaa)` `∣` `color(red)(3x^2-2x+5)`
`color(white)(aaaaaaaa)` `-----`