Section 2.4 - Real Zeros of Polynomial Functions

Essential Question(s): 

Explain the various methods of finding zeros of polynomial functions

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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.

Long Division and the Division Algorithm

• What is the basic terminology of division? (pg 214)
• What is the Division Algorithm for Polynomials? (pg 214)
• How do you use long division to find a quotient? (Ex 1 pg 215)

Remainder and Factor Theorems

• What is the Remainder Theorem? (pg 215)
• How do you use the Remainder Theorem? (Ex 2 pg 216)
• What is the Factor Theorem? (pg 216)
• What are the Fundamental Connections for Polynomial Functions? (pg 217)

Synthetic Division

• What is Synthetic Division? (pg 217)
• How do you use Synthetic Division? (Ex 3 pg 218)

Rational Zeros Theorem

• What is the Rational Zeros Theorem? (pg 218-219)
• How do you find Rational Zeros? (Ex 4 & 5 pg 218)

Upper and Lower Bounds

• Review upper and lower bounds. (pg 220)
• What are the Upper and Lower Bounds Tests for Real Zeros? (pg 220)
• How can you prove bounds for real zeros? (Ex 6 pg 220)
• How can you find the real zeros of a polynomial function? (Ex 7 pg 221)
• How can you prove the real zeros of a polynomial function lie within an interval? (Ex 8 pg 222)

Synthetic Division Process

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

• Read pages 214-223.
• Make sure to read the paragraphs between the examples.