Question

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

Answer 1

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.