1. Lesson 2.5 The Fundamental Theorem of Algebra

2. For f(x) where n > 0, there is at least one zero in the complex number system
Complex → real and imaginary
Real zeros → can see on graph
Imaginary → cannot see on graph
f(x) of degree n will have exactly n zeros (real and imaginary)
Complex zeros always occur in conjugate pairs
“If a + bi is a zero, then a – bi is also”

3. How do we find the zeros of
For a polynomial f(x) with degree n:
Find real zero(s) using calculator or Factor Theorem and Synthetic Division
If there are n real roots, stop
Divide out real zeros to obtain a 2nd degree equation
Solve 2nd degree equation for x (use Quadratic Equation if necessary)

4. Linear Factorization

5. Example 1

6. Example 2

7. HW 2-5 pg 234: 1-11 odd, 17-20, odd, 35, 37