Long Division

Question

Divide by using synthetic division. (2x^2 - 2x +3) / (x-3)

Answer 1

(2x²-2x+3)/(x-3)

 

For synthetic division we use on the outside the value of x that would make (x-3) = 0 so we use 3

 

Set this up like a division problem almost... with 3 on the left line up the coefficients of the numerator

in descending order by highest to lowest exponent... 2   -2   3  so we have...

 

    __________

3 / 2    -2    3

            6    12    bring down the first coefficient to the bottom so 2 comes down

   --------------    multiply that by the divisor 3 giving 6 which you bring up under the -2

     2     4     15   add that line to get 4... 3(4) = 12 so bring 12 up under the 3.

                         Add that line to get 15

 

The last number on the bottom (15) is the remainder.  The 2nd to last (4) is a constant.  The far left will be the

coefficient with the next higher exponent giving ...

 

This means that (2x^2 - 2x +3) / (x-3) = 2x + 4 remainder 15

 

As in regular division the remainder should be written as a fraction with as R/divisor so

 

(2x^2 - 2x +3) / (x-3) = 2x + 4 + 15/(x-3)