Wetzel                         

Math 110

3.1 – The Remainder and Factor Theorems

Dividing Polynomials –

            Long Division:   Always works, but usually not the quickest method.

            Synthetic Division:         Used when dividing by a binomial in the form   x – c

            Ex.:

            1.)                 2.) 

The Remainder Theorem –

            If a polynomial P(x) is divided by x – c, then the remainder equals P(c).

            Ex.:

            3.)  Divide.                 Find   evaluated at x = 3.

The Factor Theorem –

            A polynomial P(x) has a factor (x – c) if and only if P(c) = 0.

            Ex.:

            4.)  Determine if x – 4 is a factor of

HOMEWORK:  6th Ed.   p.290  #1-5odd, 13-17odd, 27-31odd, 37-41odd, 47-51odd, 57, 59

                           5th Ed.  p.287  #1-5odd, 11-15odd, 27-31odd, 35-39odd, 45-49odd, 55, 57