## Section 7.4 - Partial Fractions

**Essential Question(s):**

Explain the skills necessary to decompose a rational function into partial fractions.

**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.

__Partial Fraction Decomposition__

- What is a partial fraction and partial fraction decomposition? (pg 608)
- How do you write the decomposition factors? (Ex 1 pg 608)

__Denominators with Linear Factors__

- How do you decompose a fraction with distinct linear factors? (Ex 2 pg 609-610)
****They use matrices to solve. You will use algebraic methods to solve the system.**** - How do you decompose a fraction with a repeated linear factor? (Ex 3 pg 610)
****They use matrices to solve. You will use algebraic methods to solve the system.****

__Denominators with Irreducible Quadratic Factors__

- How do you decompose a fraction with an irreducible quadratic factor? (Ex 4 pg 611-612)
****They use matrices to solve. You will use algebraic methods to solve the system.**** - How do you decompose a fraction with a repeated irreducible quadratic factor? (Ex 5 pg 612)
****They use matrices to solve. You will use algebraic methods to solve the system.****

__Applications__

- How does partial fraction decomposition get used with investigating the graph of a rational function? (Ex 6 pg 613)

**STEP 3: Reading**

__Read__the following page(s) and take any extra notes as needed.

- Read pages 608 - 613.
- Make sure to read the paragraphs between the examples.