1. Warm-Up #
A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along two sides of it?
The bases on a softball diamond are 60 feet apart. How far is it from home plate to second base?
Expand it out: f(x) = -2(x + 1) (x -7)

2. Homework
Lesson 5.3_page 296 #30-48 even

3. Golden Rules of Factoring

4. Example: Factor out the greatest common factor
f(x)= 4x2 + 20x -12

5. Practice: Factor each expression
Solutions:
a.) 3(3x2 + x – 6)
b) 7(p2 + 3)
c) 2w(2w + 1)
a) f(x)= 9x2 + 3x – 18
b) f(x)= 7p2 + 21
c) f(x)= 4w2 + 2w

6. Factor Diamonds f(x)=1x² + 8x + 7 (x + 1) (x + 7) ac add multi b 7 7 1

7. Practice: Solve by a factor diamond
1) x2 + 15x + 36
2) x x

8. Factor by Grouping f(x)= 2x² – 7x – 15 2x² – 10x + 3x – 15 =0
-30
-10 3 -7
Note: you are on the right track because you have (x-5) in both parenthesis
2x(x – 5) + 3(x – 5) =0
(2x + 3)(x – 5)=0

9. Practice: Factor by Grouping
f(x)= 3x2 + 7x – 20
2) f(x)= 3x2 - 5x – 2

10. SHORTCUTS a2 + 2ab + b2 (a+b)2 a2 - 2ab + b2 (a - b)2
Example: 25x2 + 90x + 81
(5x + 9)2
a2 - 2ab + b (a - b)2
Example: 9x2 – 42x + 49
(3x – 7)2
a2 - b (a+b)(a - b)
Example: x2 – 64
(x + 8)(x – 8)

11. Practice Problems: Solve using any method
Solutions:
a) (x-6)(3x+2)
(x+2)(4x-3)
(2x+7)(2x-7)
(x+4)(2x+3)
f(x)= 3x2 – 16x – 12
f(x)= 4x2 + 5x – 6
f(x)= 4x2 – 49
f(x)= 2x2 + 11X + 12