Synthetic Division of a Polynomial

To divide a polynomial by a binomial, make sure that both the divisor and the dividend are in descending order.  [Note:  After the degree of the dividend is established, if there are any powers missing from the dividend you must insert a "place holder" in for the missing degree.]


The binomial is in the form x - c.  Identify the "c" in the binomial.  Next identify the coefficients of the terms of the dividend.  See the form below.

     5   +12    -36    -16

 To start the synthetic division, write the first coefficient below the line.           

     5   +12    -36    -16



Next, multiply the "c" by the number that is below the line and put the product below the second coefficient listed in the dividend and then add the two numbers in the second column.

     5   +12    -36    -16


            5   +22

Continue multiplying and adding in the same manner until all coefficients are divided by "c."

     5   +12    -36    -16

                 +10    +44           

            5   +22    +8

     5   +12    -36    -16

                 +10    +44   +16    

            5   +22    +8        0

To interpret the answer you must understand that the quotient will always be one degree less than the dividend.  Since the example started with a 3rd degree polynomial, the quotient (answer) will be a 2nd degree polynomial.  The numbers below the line will be the coefficients of the quotient.  Thus, the quotient for the example is 5x2    +22x    + 8.  If the last number is a number other than zero, this will be the remainder.  The example above has no remainder.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 19-Sep-2007