1. Rational Root and Complex Conjugates Theorem

2. Fundamental Theorem of Algebra
Every polynomial of degree n has exactly n roots.

3. Rational Root Theorem
Used to find possible rational roots (solutions) to a polynomial
Possible Roots : P/Q
Where P represents the factors of the constant of the polynomial and Q represents the factors of the leading coefficient

4. Rational Root Theorem

5. Find all possible rational roots and then find ones that work.

6. Another example

7. Rational Root Theorem

8. Complex Conjugates Theorem
If a + bi is a zero of the polynomial, then a – bi is a zero also.
Ex. Find the polynomial whose zeros include 3 and 2 – i

9. Find the lowest degree polynomial with the following roots

10. Find the lowest degree polynomial with the following roots