1. Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48
1) 10
2) 48
3) 7
Find the greatest common factor (GCF) of each set of numbers.
4) 6,14
5) 12,18,30
6) 4,8,15,20

2. 5.3.1 Factoring Quadratic Expressions
Objectives:
Factor a quadratic expression

3. Example 1 Factor each quadratic expression. a) 27x2 – 18x 27 x2 18 x
factor out the GCF for all terms 9 x
(3x – 2)
b) 5x(2x + 1) – 2(2x + 1)
(2x + 1)
(2x + 1)
factor out the GCF for all terms
(2x + 1)
( )
5x - 2

4. Factoring x2 + bx + c
To factor an expression of the form ax2 + bx + c, where a = 1, look for integers r and s such that r s = c and r + s = b. Then factor the expression.
x2 + bx + c =
(x + r)(x + s)

5. Example 2
Factor x2 + 12x + 27.
( ) x + 3
( ) x + 9

6. Example 3
Factor x2 - 15x - 54.
( ) x + 3
( ) x - 18

7. Example 4
Factor 5x2 + 14x + 8.
( ) 5x + 4
( ) x + 2

8. Practice Factor. 1) 5x2 + 15x 2) (2x – 1)4 + (2x – 1)x 3) x2 + 9x + 20

9. Homework
p.296 #31,35,37,39,41,43,45,49,53,57

10. Warm-Up 5 minutes Factor. 1) 3x2 - 15x 2) (3x + 7)x + (3x + 7)8

11. 5.3.2 Factoring Quadratic Expressions
Objectives:
Factor a quadratic expression
Use factoring to solve a quadratic equation and find the zeros of a quadratic function

12. Special Products Factoring the Difference of Two Squares
a2 – b2 = (a + b)(a – b)
Factoring Perfect-Square Trinomials
a2 + 2ab + b2 = (a + b)(a + b)
a2 - 2ab + b2 = (a - b)(a - b)

13. Example 1
Factor x
( ) x + 4
( ) x - 4

14. Example 2 Factor x4 - 81. ( ) x2 + 9 ( ) x2 - 9 (x2 + 9) ( ) x + 3 ( )
( ) x2 + 9
( ) x2 - 9
(x2 + 9)
( ) x + 3
( ) x - 3

15. Example 3 Factor 2x2 – 24x + 72. 2 24 72 2 ( ) x2 – 12x + 36 2( )( )
( )
x2 – 12x + 36
2( )( )
x - 6
x - 6

16. Zero-Product Property
If pq = 0, then p = 0 or q = 0.

17. Example 4 Solve . 5x2 + 7x = 0 x(5x + 7) = 0 x = 0 or 5x + 7 = 0
CHECK:
5x2 + 7x = 0
CHECK:
5x2 + 7x = 0
5(0)2 + 7(0) = 0
0 + 0 = 0

18. Example 5 Find the zeroes of the function f(x) = x2 – 5x + 6or
x - 2 = 0
x = 3
x = 2
CHECK:
x2 – 4x = x - 6
CHECK:
x2 – 4x = x - 6
32 – 4(3) = 3 - 6
22 – 4(2) = 2 - 6
9 – 12 = -3
4 – 8 = -4
-3 = -3
-4 = -4
The zeroes are located at x = 2 and x = 3.

19. Practice Find the zeroes of each function. 1) h(x) = 3x2 + 12x
2) j(x) = x2 + 4x - 21

20. Homework
p.296 #59,61,65,67,69,71,75,79,83