Polynomial p(x) and a divisor d(x) are given. Find the quotient q(x) and the remainder r(x) when p(x) is divided by d(x).
We need to find the correct multiple of to get to the level of . That multiple is .
So we multiply and subtract that from , which leaves us with . Now, how many times will go into this? .
So and we subtract out , leaving us with . Finally, we see that we need a multiple of -7 for the last step:
and we subtract this from to yield 4.
The answer is therefore:
Here is a method, it's the one I apply, it's not necessarily the one you have to use.
I see what the highest degree in p(x) is, and I find how to multiply x powered to the highest degree to get the first term of p(x).
So I'll write :
Then I'll do it again, with -10x² :
And continue, again and again...