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

1 Answer
Jun 21, 2018

What do you need to multiply 7x by to get #-x^3#?
#(-1/7)x^2# This is your first dividend term.
answer: #(-1/7)x^2-(10/49)x-(488/343)+((2822/343)/(7x+10))#

Explanation:

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