Unit D Student Success Sheet (SSS) Factoring (section 2.1)

Transcription

1 Unit D Student Success Sheet (SSS) Factoring (section 2.1) Standards: Alg , Alg , Alg Mr. Werdel Segerstrom High School Math Analysis Honors Name: Period: Mr. Werdel: Monday after school, 2 nd lunch. Mrs. Kirch: Monday Wednesday Mornings 7-8am & Wednesday Friday afterschool from 3-4pm Ms. Tamaoki: Tuesday & Thursday mornings 7:30-8am Reminders: Homework is completed in spiral bound notebook only. Homework not done in homework notebook will not be accepted. All pages in homework notebook should be labeled accordingly: Unit Concept - (title of assignment) Examples: Unit D Concept 1 Practice Quiz Unit D Concept 1 Quiz Review Unit D Concept 1-4 Practice Test Success is never final, failure is never fatal. It's courage that counts. John Wooden Concept # What we will be learning Mandatory Homework 1 Completing the square (a=1, a=not 1, fractions NOT included) Worksheet 14 1a Completing the square (a=1, a=not 1, fractions REQUIRED) Worksheet 14 2 Factoring quadratics SSS Examples 3 Factoring quadratic form SSS Examples 4 Factoring by grouping SSS Examples 5 Factoring sum and difference of cubes SSS examples 6 Factoring difference of squares SSS examples This chapter is a step back into Algebra 1 and Algebra 2 in order to focus on and refine two very important skills: Completing the Square and Factoring. Completing the square is a method that helps us to put equations in a more use-able form, as well as to solve quadratics when they don t factor. It is a skill we will be using multiple times throughout the course of the year. Factoring is vital to your success in this class for the rest of the year. In this Unit, we will be looking at regular old factoring, factoring using the sum and difference of cubes formulas (which need to be memorized!), as well as the difference of squares formula. In addition, we will factor trinomials that are in quadratic form as well as polynomials with four terms using grouping.

2 ( ) Graph: ---Unit D Student Success Sheet---Factoring (section 2.1)--- Math Analysis Completing the square (a=1, a=not 1, fractions NOT included) 2 10m 20m 87 0 Why Completing the Square? You are rearranging your terms to create a factorable perfect square trinomial Most of the time, this is an easier way to solve a quadratic than to use the quadratic formula This allows us to put quadratics in a form that is much easier to graph ( ) ( ) ( ) ( ) ( ) Solve: ( )

3 Completing the square (a=1, a=not 1, fractions required) ( ) ( ) ) ( ) ( ) ( ) Graph: ( ) Solve: ( ) ( ) ( )

4 Regular Factoring Methods for Quadratic Trinomials: (you must have one that you have MEMORIZED, here are 2 possiblities!) X-Box Method 2 3x 10x 8 Factoring Methods for Quartic Trinomials: Qualifications: Powers of trinomial must be Or (all multiples of ax 2 + bx + c, with powers of 2 1 0) These will factor just like 7a 2 4a 20 (7a+10)(a-2) Except that there will be higher powers! 7a 4 4a 2 20 (7a 2 +10)(a 2-2) Factoring with FOUR terms (grouping)

5 Factoring quadratics

6 Factoring quadratic form Quadratic form means that it looks like a quadratic trinomial, and factors like a quadratic trinomial it s just NOT a quadratic trinomial! Factoring by grouping

7 Difference of Squares ( )( ) Example 1: ( )( ) Example 2: Example 3: ( )( ) ( ) ( )( ) Example 4: ( )( ) ( )( )( ) If a polynomial does not factor, it is PRIME. The SUM OF TWO SQUARES is prime The resulting expression from the SUM and DIFFERENCE of TWO CUBES is prime Always check to make sure your answers are fully factored! Sum of Two Cubes ( )( ) Example 1: [ ] ( )( ) Example 2: [ ] ( )( ) Example 3: ( ) [ ] ( )( ) Difference of Two Cubes ( )( ) **the (-) in the original formula has no effect on the value of b!!! Example 1: [ ] ( )( ) Example 2: [ ] ( )( ) Example 3: ( ) [ ] ( )( )

8 Factoring sum and difference of cubes Factoring difference of squares