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

Question

2202 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-06T20:19:47

$Quotient=-7x^2+4x-6$ & Remainder $=7/(2x+3)$

$(-14x^3-13x^2-11)/(2x+3)$

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

$-(3/2)$ | -14 -13 0 -11
| 21 -12 18
|______
-14 8 -12 (7)
Next divide by 2.

$Quotient=-7x^2+4x-6$ & Reminder #=7/(2x+3)

Verification :
$f(-(3/2))=(-14(-(27/8)))-13(9/4)-11-7)$
$=(189/4)-(117/4)-(44/4)-(28/4)=0$

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