Explain why (x^2 - 9) divided by (x + 3) is not the same as (x - 3)

Let's divide ( ) by (x+3)

This can be divided by many methods,

1) Lets first divide it by factorizing the polynomial ( ),

We know that 

So 

Now,

And if you want to divide ( ) by (x-3),

2) We can divide the polynomial by using the long division method:     

        x - 3

      ________

x+3|

       

     ...

Let's divide ( ) by (x+3)

This can be divided by many methods,

1) Lets first divide it by factorizing the polynomial ( ),

We know that 

So 

Now,

And if you want to divide ( ) by (x-3),

2) We can divide the polynomial by using the long division method:     

        x - 3

      ________

x+3|

       

      ________

              

               

              __________

                    0

               __________

 So, ( ) divided by (x+3) yields (x-3)

and ( ) divided by (x-3) yields (x+3)