1. S ECTION 10.4 Solving Polynomials Equations in Factored Form

2. D AILY W ARM - UP Directions: Find the product. 1. (5x² – 3x)² 2. (x – 3)(3x 2 + 9 – 7x) 24x 4 – 30x 3 + 9x 2 3x 3 – 16x 2 + 30x – 27

3. 10.4 – S OLVING P OLYNOMIAL E QUATIONS IN F ACTORED F ORM Objectives: 1. Solve a polynomial equation in factored form. 2. Understand the difference between factors, solutions, and zeros.

4. V OCABULARY A polynomial in factored form is written as a product of two or more linear factors. A clue to look for is if there are multiple sets of parenthesis. Example: The factored form of x² +4x + 4 is: (x + 2)(x + 2).

5. Z ERO -P RODUCT P ROPERTY Let a and b be real numbers. If (a)(b) = 0, then a = 0 or b = 0.

6. H OW T O G UIDE : U SING THE Z ERO - P RODUCT P ROPERTY Solve the equation (x – 4)(x + 1) = 0 by the zero-product property: 1. (x – 4)(x + 1) = 0 2. (x – 4) = 0 (x + 1) = 0 3. x = 4 and x = -1 1. Set each piece equal to zero. Hint: Pieces are separated by ( ). 2. Solve each equation for x. 3. Check your solutions. ExampleExplanation + 4 +4 -1 -1

7. U SING THE Z ERO -P RODUCT P ROPERTY Solve (x – 9)(x + 8) = 0Solve (2z – 6)(z + ¾) = 0 Example: x = 9 x = -8 z = 3 z = -3/4

8. U SING T HE Z ERO -P RODUCT P ROPERTY Solve (w – 14)² = 0Solve x(2x + 8)(x – 32)=0 Example: w = 14 x = 0 x = -4 x = 32

9. Brain Break USE THIS TIME TO STRETCH OUT OR … Try these Rebus Puzzles… Too funny for wordsThe wrong end of the stick

10. F ACTORS, S OLUTIONS, AND X - INTERCEPTS For any quadratic polynomial ax² + bx + c, if one statement is true, then all 3 statements are true. 1. (x – 4) and (x + 4) are factors of x² -16 2. x = 4 and x = -4 are solutions of x² - 16 = 0 3. 4 and -4 are x-intercepts of y = x² - 16

11. F IND THE FACTORS, SOLUTIONS, AND X - INTERCEPTS OF F IND THE FACTORS, SOLUTIONS, AND X - INTERCEPTS OF Y = ( X – 3)( X + 1) x = 3 x = -1

12. F IND THE FACTORS, SOLUTIONS, AND X - INTERCEPTS OF F IND THE FACTORS, SOLUTIONS, AND X - INTERCEPTS OF Y = ( X + 4)( X - 2) x = -4 x = 2

13. R OW R ELAYS Each member of your row has a different task. Once you finish your role, pass your team’s worksheet back. The first correct row gets 2 points. Each other correct row gets 1 point. 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. DirectionsYour Starring Role

14. R OW R ELAYS : R OUND 1 (x – 1)(x + 2) = 0 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. ProblemYour Starring Role x = 1 x = -2

15. R OW R ELAYS : R OUND 2 (x – 5)² = 0 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. DebacleYour Starring Role x = 5

16. R OW R ELAYS : R OUND 3 (3z + 9)(2z – 2) = 0 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. PredicamentYour Starring Role z = -3 z = 1

17. R OW R ELAYS : R OUND 4 (6b – 18)(2b + 4)(2b + 8) = 0 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. DilemmaYour Starring Role b = 3 b = -2 b = -4

18. R OW R ELAYS : R OUND 5 n(9n + 27)(6n – 24) = 0 1 st : Set each factor equal to zero. 2 nd : Solve each equation for the variable. 3 rd : Check the work! 4 th : List the factors, solutions, and x- intercepts. 5 th : Plot the x-intercepts. QuandaryYour Starring Role n = 0 n = -3 n = 4

19. H OMEWORK pgs. 600-601 #19-24, #37-39, #44-46

20. B ONUS EXAMPLES : S OLVE THE FOLLOWING EQUATIONS Solve (x + 8)² = 0 Solve (x – 4)(x + 3) = 0 Solve x(x+3)(2x – 3) = 0 (3x – 2)(4x + 3)(x + 4) = 0 -8 4, -3 0, -3, 3/2 2/3, -3/4, -4