Section 2.5 - Complex Zeros and the Fundamental Theorem of Algebra

Essential Question(s): 

Explain the process of factoring polynomials with real coefficients using factors with complex coefficients.

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Two Major Theorems (pages 228-229)

• What is the Fundamental Theorem of Algebra?
• What is the Linear Factorization Theorem?
• What are the Fundamental Polynomial Connections in the Complex Case?
• How do you apply Fundamental Polynomial Connections? (Ex 1)

Complex Conjugate Zeros (pages 230-232)

• What is the Complex Conjugate Zeros Theorem?
• How do you find a polynomial from given zeros? (Ex 2 & 3)
• How do you factor polynomials with complex zeros? (Ex 4)
• How can you find complex zeros? (Ex 5 pg 231)

Factoring with Real Number Coefficients (pages 232 - 233)

• What are irreducible factors?
• What are factors of a polynomial with real coefficients?
• How are irreducible factors used when factoring polynomials? (Ex 6)
• What can you say about polynomial functions of odd degree?

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 228-233.
• Make sure to read the paragraphs between the examples.