09 Factoring Special Patterns.notebook
­x2
x
1
­x
2
x
x
November 01, 2011
­x
­1
Factor: x2 + 6x + 9
2
x
x
x
x
x
x
x
1 1 1
1 1 1
1 11
Mar 25­8:02 AM
Factor x2 + 6x + 9 algebraically
Oct 30­11:08 PM
1
09 Factoring Special Patterns.notebook
x
1
­x
­x2
x
x2
November 01, 2011
­x
­1
Factor: 4x2 ­ 12x + 9
x2
x2
­x
­x
­x
x2
x2
­x
­x
­x
­x
­x
­x
­x
­x
­x
1 1 1
1 11
1 11
Mar 25­8:02 AM
Factor 4x2 ­ 12x + 9 algebraically
Oct 30­11:09 PM
2
09 Factoring Special Patterns.notebook
­x
x
1
2
­x
2
x
x
November 01, 2011
­x
­1
Factor: 25x2 ­ 30x + 9
Mar 25­8:02 AM
Factoring Special Quadratics
1. Perfect Square Trinomial
(a) a2 + 2ab + b2 = (a + b)(a + b)
= (a + b)2
(b) a2 ­ 2ab + b2 = (a ­ b)(a ­ b)
= (a ­ b)2
Note: 1. Standard methods, such as alge­tiles or
decomposition (SPI) will also work, but may take
longer.
2. It is critical to check the 2ab term to make sure you
have a perfect square, or verify your final answer.
Mar 29­11:14 AM
3
09 Factoring Special Patterns.notebook
November 01, 2011
Ex.1 Factor using a pattern (if possible)
(a) x2 + 12x + 36
(b) x2 + 13x + 36
(c) 4x2 ­ 20x + 25
Mar 29­11:16 AM
­x
x
1
2
­x
2
x
x
­x
­1
Factor: 4x2 ­ 9
x
x
x
x
2
x
2
2
­x
­x
­x
2
­x
­x
­x
x
x
x
x
x
­1 ­1 ­1
­1 ­1 ­1
­1 ­1 ­1
Mar 25­8:02 AM
4
09 Factoring Special Patterns.notebook
November 01, 2011
Factor 4x2 ­ 9 algebraically
Oct 30­11:09 PM
x
­x
1
2
­x
2
x
x
­x
­1
Factor: 9x2 ­ 16
Mar 25­8:02 AM
5
09 Factoring Special Patterns.notebook
November 01, 2011
Factor 9x2 ­ 16 algebraically
Oct 30­11:09 PM
2. Difference of Squares
(the order of the binomials
a2 ­ b2 = (a + b) (a ­ b) = (a ­ b) (a + b) does not matter)
Ex.2 Factor (a) k2 ­ 121
(b) 81m2 ­ 144
Mar 29­11:17 AM
6
09 Factoring Special Patterns.notebook
November 01, 2011
Ex.3 Factor using a special pattern:
(a) 25d2 ­ 144
(b) 16x2 + 24xy + 9y2
(c) 18p2q ­ 60pq + 50q
(d) 98a2 ­ 32b2
Mar 26­8:24 AM
Assigned Work:
p. 230­231 # 3bc, 5, 6, 7, 10, 11, 14
Mar 26­9:06 AM
7
09 Factoring Special Patterns.notebook
November 01, 2011
Nov 1­9:14 AM
Nov 1­9:17 AM
8
09 Factoring Special Patterns.notebook
November 01, 2011
Nov 1­9:25 AM
Nov 1­9:26 AM
9
09 Factoring Special Patterns.notebook
November 01, 2011
Nov 1­9:28 AM
10