Question

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

Answer 1

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

Explanation:

`(-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`