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

Feb 14, 2017

$- 3 x - 1 + \left(\frac{16}{x - 2}\right)$

#### 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 $\left(x - 2\right)$ by $\left(- 3 x\right)$ to get $\left(- 3 {x}^{2} + 6 x\right)$, and then we subtract it from the dividend $\left(- 3 {x}^{2} + 5 x + 14\right)$ to get $\left(- x\right)$

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

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

so now you have a quotient $\left(- 3 x - 1\right)$ and your remainder $\frac{16}{x - 2}$
so your answer is $- 3 x - 1 + \left(\frac{16}{x - 2}\right)$