1. Today’s Character Counts Quote of the Day: Respect Monday, 10/13/14 Self-respect is the fruit of discipline; the sense of dignity grows with the ability to say no to oneself. – Abraham Joshua Heschel

2. Today’s agenda: Monday, 10/13/14 Notes Factoring quadratic polynomials –Coefficient = 1 or common factor –No linear term –Standard form / not standard form Assignment Problem Set 2.01 (1 – 12)

3. Notes: Factoring Quadratics Key definitions: Polynomials –expressions that have terms: variables to whole number powers Quadratics – polynomials that have a highest power of two on the variable Terms are expressions that add or subtract Factors (n) are expressions that multiply or divide To factor (v) means to find the things that multiply to equal the given expression

4. Notes: Factoring Quadratics Key concept: Factoring is the backwards distributive property We factor to turn a sum into a product (zero product property) In order to factor well (and easily) you need two skills: Factoring out common factors Solving puzzles about sums and products

5. Key skill: Factoring out common factors Remember the distributive property: The simplest type of factoring is to look for common factors and then use the backwards distributive property

6. Key skill: Factoring out common factors Example: find the common factors Now use the backwards distributive property

7. Key skill: Factoring out common factors Try these for yourself:

8. Key skill: solving simple number puzzles Key concept: The second skill you need is to be able to solve simple number puzzles like this: Can you figure out the pattern? 2 3 6 5 -4 5 -20 1 1 0 -2

9. Key skill: solving simple number puzzles Key concept: Try these for yourself: Here’s the master note: 1 6 6 7 -2 10 -20 8 18 3 54 21 -4 4 -16 0 a b ab a+b

10. Putting the skills together 1. Write the quadratic in standard form 2. Put the constant term in the top of a “diamond puzzle”, and the linear coefficient in the bottom 3. Solve the diamond puzzle 4. Use the left and right numbers from the puzzle to rewrite the linear term 5. Factor by grouping (look for common factors twice)

11. Putting the skills together Example: 10 2 20 12 Zero Product Property