Algebra 1
Name: _______________________________
Unit 8: Lesson 6
Date: _________________ Period: _______
Factoring Special Polynomials (10.7)
Method: Difference of Two Squares (DOTS)
Essential Questions:
 How does recognizing patterns in polynomials help you factor completely??
 How do you know that a polynomial is prime?
 Why must one side of an equation be zero in order to solve by factoring?
Goal:
 Students will solve and factor binomials in the form a  b .
2
2
 Students will solve and factor perfect square trinomials.
Key Ideas / Vocabulary:
 Difference of Two Squares (DOTS)
Formula:
a  b  (a  b)(a  b)
2
Note:
2
Example:
9 x 2  16  (3x  4)(3x  4)
your answer can also be in the form (a  b)(a  b) since multiplication is _____________
 Perfect Square Trinomials
Example:
x 2  8x  16  ( x  4) 2
25a 2  60ab  36b2  (5a  6b)2
Section 1: Factor each binomial using “DOTS.”
1) Factor:
m2  4
YT 1) Factor:
f 2 9
2) Factor:
4 p 2  25
YT 2) Factor:
36 y 2  1
3) Factor:
25  49 x2
YT 3) Factor:
4  9w 2
4) Factor:
 121 a 2  16 b2
YT 4) Factor:
 169 x2  81y 2
5) Factor:
100 g 2  49
YT 5) Factor:
p 2  64
Section 2: Factoring “Perfect Square Trinomials.”
6) Factor:
x2  4 x  4
YT 6) Factor:
y 2  8 y  160
7) Factor:
16a 2  24ab  9b2
YT 7) Factor:
9m2  60mn  100n2
Section 3: Solve polynomials with fractions.
8) Solve:
x2 
1
16
Set = 0 ?
YT 8) Solve:
Factored?
r2 
1
4
2k 2  10k 
25
0
2
Set = 0 ?
Factored?
YT 9) Solve:
2
1
s2  s   0
3
9
Check ?
Homework:
“Factoring” Packet
Factored?
Check ?
Check ?
9) Solve:
Set = 0 ?
# 101-120 ALL
Ticket Out/Lesson Summary:
Explain how you could use the acronym “DOTS” as a checklist to factor certain binomials.
Set = 0 ?
Factored?
Check ?