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

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

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

4. What 2 numbers multiply to make -8?
Solve
Must be equal to zero.
–3b b
–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

5. 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

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

7. [5(- 2 5 ) + 2][3(- 2 5 ) – 4] = 0 Check: if b =
Solve
[5( ) + 2][3( ) – 4] = 0
(–2 + 2) [3( ) – 4] = 0
0[3( ) – 4] = 0
0 = 0 TRUE
and [5( 4 3 ) + 2][3( 4 3 ) – 4] = 0
( )(4 – 4) = 0
( )(0) = 0
0 = 0 TRUE

8. Solve
3 , 4 -
Answer:
x =
Example 4-4b

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

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

11. Homework
368/17-25 odd