1. 1 Algebra 2: Section 6.5 The Remainder and Factor Theorems (Day 2)

2. 2 The Factor Theorem A polynomial has a factor x - k iff f(k)=0. The number k is also called “a zero” of the function. –ie: answer/remainder will = 0 These facts can be used with synthetic division to aid in factoring more complex polynomials.

3. 3 General Steps to Factor Polynomials Use synthetic division to factor the polynomial until one factor is a quadratic (highest power is 2) Use one of the following methods to solve the quadratic –Factor –Quadratic Formula Remember we are using “x - k”

4. 4 Examples Factor the polynomial given that f(k)=0 (HINTS: you know “k” is a zero)

5. 5 First use synthetic division to factor given that -4 is one zero (this also means x+4 is a factor) Rewrite the polynomial in Factored form Factor the quadratic using trial & error

6. 6 Examples Given one zero of the polynomial, find the other zeros. –ie: Solve

7. 7 First use synthetic division to factor given that -5 is one zero Rewrite the polynomial in Factored form (and set equal to zero) Factor the quadratic using trial & error Solve each factor, set each equal to zero

8. 8 Examples Given one zero of the polynomial, find the other zeros.

9. 9

10. 10 Use the quadratic!

11. 11 Homework p.357 #40-56 evens Go over #55