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

1 Answer
Oct 6, 2017

Answer:

#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#