1. Warm-up: Factor 3x x - 14
a = 3 b = c = -14
Use the X-box: x 7
a·c
3x2
21x
-42 3x X 21 -2
-2x
-14 19 -2 b
(3x – 2)(x + 7)

2. Agenda
Warmup
Check Homework
Notes 7-4C
Assignment

3. Lesson 7.4C Learning Target:
More solving equations in the form ax2+bx+c = 0

4. 18 X 9 2 11 (x + 3)(3x + 2) = 0 3x2 9x 2x 6 EX 1: 3x2 + 11x + 6 = 0 x
No common factors!
a = 3 b = c = 6
Use the X-box: x 3
a·c
3x2 9x 18 3x X 9 2 2x 6 11 2 b
(x + 3)(3x + 2) = 0

5. (x + 3)(3x +2) = 0 3x + 2 = 0 x + 3 = 0 x = -3 3x = -2 x = -2/3
Now, set each factor equal to zero and solve:
3x + 2 = 0
x + 3 = 0
x = -3
3x = -2
x = -2/3

6. EX 2: 4x2 + 19x – 5 = 0
No common factors!
a = 4 b = c = -5
Use the X-box: x 5
a·c
4x2
20x
-20 4x X 20 -1
-1x -5 19 -1 b
(x + 5)(4x – 1) = 0

7. (x + 5)(4x – 1) = 0 4x – 1 = 0 x + 5 = 0 x = -5 4x = 1 x = 1/4
Now, set each factor equal to zero and solve:
4x – 1 = 0
x + 5 = 0
x = -5
4x = 1
x = 1/4

8. EX 3: 4x2 – 20x + 21 = 0
No common factors!
a = 4 b = c = 21
Use the X-box: 2x -7
a·c
4x2
-14x 84 2x X -6
-14
-6x 21
-20 -3 b
(2x – 7)(2x – 3) = 0

9. (2x – 7)(2x – 3) = 0 2x – 3 = 0 2x – 7 = 0 2x = 7 2x = 3 x = 3/2
Now, set each factor equal to zero and solve:
2x – 3 = 0
2x – 7 = 0
2x = 7
2x = 3
x = 3/2
x = 7/2

10. Are you a Master? Solve the following equations.
#1: Solve 4x2 + 1x - 14 = 0
#2: Solve 12x = 23x
x= -2, x = 7/4 or 1.75
x= 2/3, x = 5/4 or 1.25

11. Remember????? Solving polynomials with boxes
EXAMPLE 4: Factor 4x + 8
Make a rectangle with two boxes, putting each term in its own box
2. Label the width with the GCF of the terms x 2
4 (x + 2)= 0
X + 2 = 0 4x 8 4
X = -2

12. Factoring polynomials with boxes
Remember?????
Factoring polynomials with boxes
EXAMPLE 5: Factor x2 – 5x
Make a rectangle using these terms x
- 5
x (x - 5) x2
-5x x
X = 0 x – 5 = 0
x = 5

13. What is the difference between FACTOR and SOLVE?????
So wait?????
What is the difference between FACTOR and SOLVE?????

14. Assignment 7-4C: