K. Laws
Algebra II 6.7 Notes Day 1
Using the Fundamental Theorem of Algebra
Goals:
 I will use the fundamental theorem of Algebra to determine how many
solutions a polynomial should have.
 I will use synthetic or long division to find all solutions of a polynomial.
Review:
 When a real number and an imaginary number are written as a sum it is
called a _______________________________.
Complex Conjugate Theorem
If a + bi is a zero/solution of the function, then a – bi is also a zero/solution.
The Fundamental Theorem of Algebra
Every polynomial of degree “n” where n > 0 has at least one solution in the
complex numbers.
o A polynomial with the nth degree will have n solutions.
o They do not have to be distinct solutions (Can be repeated)
Ex 1
Find all the zeros of the polynomial (Real and Complex).
𝑔(𝑥) = 𝑥 4 + 3𝑥 3 − 8𝑥 2 − 22𝑥 − 24
Homework: