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 To start the synthetic
division, write the
5 +12 _______________ Next, multiply the "c" by
the number that is below the line and put the
5 +12 5 Continue multiplying and adding in the same manner until all coefficients are divided by "c."
5 +12 5 +22
5 +12 5 +22 +8
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
5x The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 19-Sep-2007 |