1. Unit 4 Algebra Investigations Lesson 2: Factoring Polynomials and Expanding Polynomials MM1A2f. Factor expressions by greatest common factor, grouping, trial & error, and special products. MM1A3c. Use a variety of techniques, including technology, tables, & graphs to solve equations resulting from investigation of x ² + bx+c = 0 Notes 2.6: Factor x 2 + bx + c

2. Factoring x 2 + bx + c Algebra: x 2 + bx + c = (x + p)(x + q) provided ______ = b and ____ = c. Example: x 2 + 6x + 5 = (_____) (_____) because ________ = 6 and ______ = 5

3. Factoring Tricks The SIGNS of the terms in your trinomial will give you a clue as to it’s factored form!! x 2 + bx + c When b and c are positive x 2 + bx + c (x + _)(x + _) When b is negative and c is positive x 2 - bx + c (x - _)(x - _) When b is positive and c is negative x 2 + bx - c (x + Larger )(x – smaller ) When b is negative and c is negative x 2 - bx - c ( x – larger )(x + smaller )

4. Preview Practice Examples:

5. (Ex 1) Factor when b and c are positive. Factor: x 2 + 10x + 16 Factor: y ² + 6y + 5

6. (Ex 2) Factor when b is negative and c is positive. Factor: a 2 – 5a + 6 Factor: w ² - 10w + 9

7. (Ex 3) Factor when b is positive and c is negative. Factor: y 2 + 3y – 10 Factor: x ² + 6x - 7

8. Ex: 4 Solve polynomial equation x ² - 4x = 21

9. Checkpoint: Factor the trinomial. 1. x 2 + 7x + 12 2.x 2 + 9x + 8 3.x 2 – 12x + 27

10. Checkpoint: Factor the trinomial. 4. x 2 – 9x + 20 5. y 2 + 4y – 21 6. z 2 + 2z – 24

11. Assignment Pg. 83 # 1-9, 11 – 18 (odd)