1. Sec 4: Factored Polynomials and their Roots
Learning Target: I will determine the number of roots in a factored polynomial function. I will identify all real and complex roots of the factored polynomial.
QC Practice
Sec 4: Factored Polynomials and their Roots

2. Ex 1: How Many Roots?
Each of the polynomial functions are already factored. How many solutions does each function have?
x(2x – 1) = 0
x(3x² - 3)(2x + 1)³ = 0
(5x – 1)(4x³ + 2)²(x² + 8) = 0

3. Ex 2: Find all Real and Complex Solutions. Label each.
x(2x – 1) = 0
x(3x² - 3)(2x + 1)³ = 0
(5x – 1)(4x³ + 2)²(x² + 8) = 0
X² + 4x – 5 = 0
Hint: If the polynomial is already factored you just have to put each part equal to 0 and solve!

4. Ex 3: x(x² + 8)(3x – 9)³ = 0 Number of Solutions Work to get solutions
Real Solutions
Complex Solutions
(if they can be found)

5. Ex 3: Quality Core Practice
Ask Yourself:
How many solutions are there?
In order to cross the x-axis, the solutions must be REAL. Did I pick those out?

6. Ex 4: Holy Cow! Find all solutions of
P.S. – You can find the complex solutions!

7. HOMEWORK
Solutions to Factored Polynomials worksheet