Polynomial long division, how do I do it?

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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) 
 
 
 
Giulio P. GCSE Maths tutor, A Level Maths tutor, A Level Economics tu...

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