Question

How do you divide `( -3x^3 + 5x + 14) div (x-2)`?

Answer 1

`-3x-1 + (16/(x-2))`

Explanation:

diving by long division, you want to try and eliminate each term in the dividend (`-3x^2 + 5x + 14)` one by one until you get a remainder that you can no longer divide by

we multiply `(x-2)` by `(-3x)` to get `(-3x^2+6x)`, and then we subtract it from the dividend `(-3x^2 + 5x + 14)` to get `(-x)`

we keep doing this until we get a remainder that we can no longer divide by

there's nothing that you can multiply by `(x-2)` that can make it any simpler, 16 is as far as we go

so now you have a quotient `(-3x-1)` and your remainder `(16)/(x-2)`
so your answer is `-3x-1 + (16/(x-2))`