Divide by using synthetic division

(x³ + 3x² - 34x + 48) divided by (x - 3)

Put a 1 before the first term.  It is already
in descending order.

1x³ + 3x² - 34x + 48

Erase the variables:

From (x - 3), change the sign of -3 to +3, or 3, and write this:

 3|1   3 -34  48
  |_____________

Bring down the 1

 3|1   3 -34  48
  |             
   1

Multiply the 1 at the bottom by the 3 on the far left, getting
3, and so  we put the 3 ABOVE AND TO THE RIGHT OF the 1 we just
brought down.  So we have this:

 3|1   3 -34  48
  |    3        
   1

Now we add the column with the 3 and the 3 and get 6. So we write
that 6 under the two 3's we just added,

 3|1   3 -34  48
  |    3              
   1   6 

Now we add the column with the 3 and the 3 and get 6. So we write
that 6 under the two 3's we just added,

Now we multiply the 6 by the 3 at the far left, getting 18, and write
that ABOVE AND TO THE RIGHT of the 6

 3|1   3 -34  48
  |    3  18          
   1   6 

Now we add the -34 and the 18 and get -16, so we write that under
their column:

 3|1   3 -34  48
  |    3  18          
   1   6 -16 

Then we multiply the -16 by the 3 at the far left, getting -48.
Then we write that ABOVE AND TO THE RIGHT of -16:


 3|1   3 -34  48
  |    3  18 -48      
   1   6 -16    

Only one more thing to do.  Combine the 48 and the -48 and get 0.


 3|1   3 -34  48
  |    3  18 -48      
   1   6 -16   0

Now we have to interpret the synthetic answer:

The last number, 0 is the remainder.

The other three numbers 

   1   6 -16

are a synthetic form of the quotient, remembering 
it will be a polynomial of one less degree than 
the original polynomial. So since the original 
polynomial has degree 3, it will have degree 2 
and so will begin with an x² term. So the
quotient i

   1   6 -16

   |   |  |

   1x²+6x-16

Then we write the answer and we would put the remainder
over the divisor:

 x² + 6x - 16 

Edwin