`3x+11` | |||

`x-2` | `{:)` | `3x^2+5x-8` | |

`3x^2-6x` | We multiply `(x-2)` by `3x =` ` 3x^2-6x`, giving `3x^2` as the first term. | ||

`11x-8` | `5x-(-6x)` ` = 5x+6x` `=11x`. Then bring down the `-8`. | ||

`11x-22` | Multiply `(x-2)` by `11=` `11x-22`. | ||

`14` | `-8-(-22) ` `= 14`. This is the remainder. |

Thus, we can conclude that:

3

x^{2}+ 5x− 8 = (x− 2)(3x+ 11) + 14

where the quotient `q(x) = 3x + 11` and the remainder `R = 14`.

We can also write our answer as:

`(3x^2+5x-8)-:(x-2)` `=(3x+11)+14/(x-2`