1. Using theorems to factor polynomials

2.  If a polynomial f(x) is divided by x-k, then the remainder r = f(k)  This is saying, when you divide (using synthetic division) by some factor k, the remainder is the same as what you would get when you substitute the value of k.  Synthetic Division and Synthetic Substitution are the same thing – plugging a value in gets the same thing as if you were to divide by that factor.

3.  The divisor must be in the form x-k.  Examples:  If you were asked to divide by x+1, you would plug in or synthetically divide by -1  x+1=0 then x=-1  Divide by x-6, means to plug in or divide by +6  x-6=0, then x=6  Divide by x+3, means to plug in or divide by _______  x+3 = 0, then x = ______

4. 1) Divide using synthetic division. 2) Divide

5.  Example……..

6.  A polynomial f(x) has a factor x-k, if and only if f(k)=0.  Examples:  If f(3)=0, then x=3 is a zero and x-3 is a factor  If f(-2)=0, then x=-2 is a zero and x+2 is a factor  If f(13) does not equal zero, then 13 has a remainder  If f(-5)=0, then ______ is a zero and _____ is a factor.

7.  Find the other zeros given f(2)=0 for:  Do we plug in 2 or -2 for synthetic division?  f(2) = 0, so x=2 is a zero and x-2 is a factor so we plug in x=2 in the synthetic division.  Practice pg 87 #14 and/or 18