# How do you divide (-x^3 - 5x^2 – 12x – 6 )/((7x + 10 )?

Jun 21, 2018

What do you need to multiply 7x by to get $- {x}^{3}$?
$\left(- \frac{1}{7}\right) {x}^{2}$ This is your first dividend term.
answer: $\left(- \frac{1}{7}\right) {x}^{2} - \left(\frac{10}{49}\right) x - \left(\frac{488}{343}\right) + \left(\frac{\frac{2822}{343}}{7 x + 10}\right)$

#### Explanation:

Each time you have to find what you need to multiply 7x by to get the lead term of the division.
For example, $\left(- \frac{1}{7}\right) {x}^{2} \left(7 x + 10\right) = - {x}^{3} - \left(\frac{10}{7}\right) {x}^{2}$
when this is subtracted from the original polynomial the result is
$\left(- \frac{25}{7}\right) {x}^{2} - 12 x$
Now find what you need to multiply 7x by to get $\left(- \frac{25}{7}\right) {x}^{2}$
To do this solve $7 x y = \left(- \frac{25}{7}\right) {x}^{2}$ for y, this is the next term for your dividend.
$\left(- \frac{10}{49}\right) x \left(7 x + 10\right) = \left(- \frac{25}{7}\right) {x}^{2} - \left(\frac{100}{49}\right) x$
subtract this from the remaining polynomial and drop down the next term.