# How do you use synthetic division to divide (-14x^3-13x^2-11) / (2x+3)?

Oct 6, 2017

$Q u o t i e n t = - 7 {x}^{2} + 4 x - 6$ & Remainder $= \frac{7}{2 x + 3}$

#### Explanation:

$\frac{- 14 {x}^{3} - 13 {x}^{2} - 11}{2 x + 3}$

$\left(2 x + 3\right) = 2 \left(x + \left(\frac{3}{2}\right)\right)$
Let us divide it in two steps.
First by (x+(3/2)) and then by 2.
For $x = - \left(\frac{3}{2}\right)$ using synthetic division :

$- \left(\frac{3}{2}\right)$ | -14 -13 0 -11
| 21 -12 18
|______
-14 8 -12 (7)
Next divide by 2.

$Q u o t i e n t = - 7 {x}^{2} + 4 x - 6$ & Reminder =7/(2x+3)

Verification :
f(-(3/2))=(-14(-(27/8)))-13(9/4)-11-7)#
$= \left(\frac{189}{4}\right) - \left(\frac{117}{4}\right) - \left(\frac{44}{4}\right) - \left(\frac{28}{4}\right) = 0$