Synthetic Division

We learned in class that Synthetic Division is a shorter method of polynomial division. When using this method, the arrangement of the coefficients of f(x) should be in a descending order of power and substitute the missing terms with zero. 

    Example: 
          
      Divide 3x³ – 2x² + 3x – 4 by x – 3 
         

•First, write down all the coefficients, and put the zero from x – 3 = 0 (so it`ll be x = 3) at the left.
•Next, 'drop' the first coefficient.
•Multiply the number by the potential zero (which is 3), carry up to the next column, and add down.
•Repeat this process.
•Repeat this process again until you reach the end.

Hence, we`ll get 68 as our remainder. Because we began with a polynomial of degree 3 and then divided by x – 3, we are left with a polynomial of degree 2. Then the bottom line symbolized the polynomial 3x<sup>2</sup> + 7x + 24 with a remainder of 68. Put the final result into the required "mixed number" format, we`ll get the answer:

Another example:

         Divide