Find the remainder when  is synthetically divided by a + .

Change the sign of the  to 

|2  -3   4   3
   |             
                    
Bring down the 2

|2  -3   4   3
   |             
    2             

Multiply the 2 by the  to get -1
Write -1 above and to the right of the 2:

|2  -3   4   3
   |   -1        
    2             

Combine the -3 and the -1, getting -4.
Write -4 at the bottom beside the 2 

|2  -3   4   3
   |    1        
    2  -4   

Multiply the -4 by the  to get -2
Write -2 above and to the right of the -4:

|2  -3   4   3
   |    1  -2    
    2  -4          

Combine the 4 and the -2, getting 2.
Write 2 at the bottom beside the -4: 

|2  -3   4   3
   |    1  -2    
    2  -4   2   

Multiply the 2 by the  to get -1
Write -1 above and to the right of the 2:

|2  -3   4   3
   |    1  -2  -1
    2  -4   2   

Combine the 3 and the -1, getting 2.
Write 2 at the bottom beside the 2: 

|2  -3   4   3
   |    1  -2  -1
    2  -4   2   2

The synthetic division is now complete,
and the remainder is the right-most term 
on the bottom line.  So the answer is 2.

The quotient is gotten from the first three
numbers on the bottom line and is interpreted
as 

2x² - 4x + 2.

But you were only asked to give the remainder
which is the right-most number on the
bottom line of the synthetic division. So
the answer is 2.

Edwin
 

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