SOLUTION: how is dividing a polynomial by a binomial similar to or different from the long division you learn in elementary school?

Question 442319: how is dividing a polynomial by a binomial similar to or different from the long division you learn in elementary school?
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Let's start off basic. Let's say you are dividing 4 into 43.
then 4 | 43 How many times does 4 go into 4? 1. So take 4*1 and subtract it from your first spot. Giving you: How many times does 4 | 3? 0. So we multiply 4 by 0 and add the 3. Since we'd keep repeating the process we'd say the answer is 10, with a remainder of 3. This 3 can also be written as 3/4, the remainder over the divisor.
Let's apply this to polynomial division.
Divide x+1 into 2x^2+4x-3.
How many times does x go into 2x^2? times.
so 2x(x+1) = 2x^2 +2x and so we subtract that from our original.
So we are left with 2x -3. We play the same game. How many times does x go into 2x? times.
So we take 2(x+1) = 2x+2 and we subtract that from our last total. so [2x-3] - [2x+2] = -5.
We are left with a remainder of -5, but just like we did in our "numerical" example, we can write the remainder as a fraction. In this case, -5/x+1.
So our complete answer is for this made up problem. It's the same process, just they're xs.
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