Review: 6.5b Mini-Quiz 1. Solve: 9x2 – 100 = 0

Objective: Students will solve quadratic equations of the form ax2 + bx + c = 0 by factoring or grouping.

Solving Quadratic Equations by Factoring or Grouping Chapter 6 – Factoring and Solving Equations Section 5c Solve equations of the form ax2 + bx +c = 0

What 2 numbers multiply to make -8? Solve Must be equal to zero. –3b2 + 5b –3b2 + 5b How? Now factor. (15b )(b ) or (5b )(3b ) What 2 numbers multiply to make -8? -8 and 1 or 1 and -8 or 8 and -1 or -1 and 8 or -4 and 2 or 2 and -4 or 4 and -2 or -2 and 4 Try them all in every possibility above until you find the answer. OR Example 4-4a

Factor by grouping. a = 15 and c = –8 therefore ac = –120 What 2 numbers multiply to make -120 and add to make –14? 6 and –20 Replace -14b with 6b – 20b Group 15b2 + 6b – 20b – 8 = 0 (15b2 + 6b) – 1(20b + 8) = 0 3b(5b + 2) – 4(5b + 2) = 0 6b –20b –14b TRUE

Now that the equation is factored, SOLVE IT. Answer: The solution set is b = Check your answers. Example 4-4a

[5(- 2 5 ) + 2][3(- 2 5 ) – 4] = 0 Check: if b = Solve [5(- 2 5 ) + 2][3(- 2 5 ) – 4] = 0 (–2 + 2) [3(- 2 5 ) – 4] = 0 0[3(- 2 5 ) – 4] = 0 0 = 0 TRUE and [5( 4 3 ) + 2][3( 4 3 ) – 4] = 0 ( 20 3 + 2)(4 – 4) = 0 ( 20 3 + 2)(0) = 0 0 = 0 TRUE

Solve 1 5 3 , 4 - Answer: x = Example 4-4b

Lesson Summary: Objective: Students will solve quadratic equations of the form ax2 + bx + c = 0 by factoring or grouping.

Preview of the next Lesson: Objective: Students will solve quadratic equations of the form ax2 + bx + c = 0 by factoring Perfect Square Trinomials.

Homework 368/17-25 odd