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.
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)
