# Polynomial long division, how do I do it?

Polynomial long division is how to divide long functions f(x), called the dividend, by another function g(x), called the divisor. Which could lead to having a remainder, if it doesn't divide perfectly.

Polynomial long division is how to divide long functions f(x), called the dividend, by another function g(x), called the divisor. Which could lead to having a remainder, if it doesn't divide perfectly.

Luckily there is one simple method to follow,

Let's divide f(x) = x^2+2x+5

by g(x) = x-2

First write it out like

____

g(x) | f(x)

__________

x-2 | x^2+2x+5

Now only look at the the first term in f(x), which is x^2, and our first term in g(x) which is x.

how many times does x go into x^2? The answer is x times thus we write x on top of our function, like this:

x

___________

x-2 | x^2+2x+5

Then multiply x^2 by our divisor x - 2 to get x^2-2x, and write it below the function like this:

x

____________

x-2 | x^2+2x+5

_____________

x^2 -2x

Now we simply find x^2+2x minus (x^2-2x) = 4x

So add the 4x on a new row below, but also don't forget to carry down the + 5 term from our dividend, thus it should now look like this.

x

__________

x-2 | x^2+2x+5

___________

x^2 -2x

___________

4x +5

Now it is as if we are dividing 4x + 5 by x - 2, so we ask the same question again, how many times does x go into 4x, the answer is 4 times, thus write + 4 at the top

x + 4

__________

x-2 | x^2+2x+5

___________

x^2 -2x

___________

4x +5

And then multiply 4 by x -2 and write it below, like this

x + 4

__________

x-2 | x^2+2x+5

___________

x^2 -2x

___________

4x +5

___________

4x - 8

Now find 4x+5 minus (4x -8) = 13 and write it below

x + 4

__________

x-2 | x^2+2x+5

___________

x^2 -2x

___________

4x +5

___________

4x - 8

___________

13

Since we can no longer divide we are left with the remainder which is is 13/(x-2)

Thus the solution is what we have at the top plus the remainder,

the solution is

x + 4 + 13/(x-2)