1. Chapter 5 – Quadratic Functions and Factoring
5.5 – Factoring Using Special Patterns

2. 5.5 – Factoring Using Special Patterns
Today we will be learning:
Factoring using special patterns

3. 5.5 – Factoring Using Special Patterns
Some quadratic expressions can be factored using special patterns.
Example: (x + 5)(x – 5). Find the product using FOIL.

4. 5.5 – Factoring Using Special Patterns
Difference of Two Squares Pattern
Algebra: a2 – b2 = (a + b)(a – b)
Example: x2 – 4 = (x + 2)(x – 2)

5. 5.5 – Factoring Using Special Patterns
Example 1
Factor the expression.
m2 – 64
p2 – 49
16n2 – 25

6. 5.5 – Factoring Using Special Patterns
To see another special pattern, find the product of (x + 3)2 using FOIL.

7. 5.5 – Factoring Using Special Patterns
Perfect Square Trinomial Patterns
Algebra: a2 + 2ab + b2 = (a + b)2
Example: x2 + 14x + 49 = (x + 7)2
Algebra: a2 – 2ab + b2 = (a – b)2
Example: x2 – 10x + 25 = (x – 5)2

8. 5.5 – Factoring Using Special Patterns
Example 2
Factor the expression.
m2 + 12m + 36
16p2 + 40p + 25
9n2 – 24n + 16

9. 5.5 – Factoring Using Special Patterns
Example 3
Factor 4m2 – 24m + 36

10. 5.5 – Factoring Using Special Patterns
Example 4
Solve 4r2 – 20r = -25

11. 5.5 – Factoring Using Special Patterns
Example 5
The time (in seconds) it takes a ball to hit the ground after dropping it from the top of a 64 foot building can be found using the function h = -16t where h is the height of the ball. Find the length of time it takes for the ball to reach the ground (h = 0).

12. 5.5 – Factoring Using Special Patterns
HOMEWORK
5.5 Worksheet
Odd Numbers

13. 5.5 – Factoring Using Special Patterns
CLASSWORK/HOMEWORK
5.5 Worksheet
Even Numbers