We will be working with the equation
divided by x+1 for this example.
We will begin like with normal division by taking the first term of the divisor,
(the x) and dividing by the first term of the dividend,
(the )
Dividing these
two would get me an x so that is the first thing in the answer. Then we carry the
x that is the answer back to the divisor and get
because our answer term x and
the x at the beginning of the divisor multiply to make x squared. We then multiply
x with the 1 and get 1x. These two terms go right under the
. After this we put an equals bar,
change the signs in the second line, and add down the numbers.
If we are doing everything right the first terms will always cancel eachother out at this point in polynomial long division.
The second term, -9x and -1x will combine into -10x and we then bring down - 10 at this point.
Then we just have -10x-10 at the bottom of our equation. We then start working from the bottom of our equation.
-10x divided by x is -10 so that term gets added to the top making the answer x-10.
Then you multiply -10 by the leading x in the divisor and get -10x which we again switch the signs of to make them cancel out.
Then we also multiply -10 by the following 1 in the divisor and get -10. We again get an equal sign below,
and change the signs to cancel out the rest of our terms. This means the end result and answer on top is simply x-10.
(Long Polynomial Division, 2021)
This video explains the process and shows more examples.