1. Factoring with DOS

2. Learning Intention/Success Criteria
LI: We are learning to factor quadratics using difference of squares (DOS) SC: I know how to -recognize if a quadratic can be factored -identify the roots and y-intercept of a quadratic -identify the solutions of the equation by factoring -square and square root numbers -find the GCF -check my work by multiplying binomials

3. Example 1a: Factor x2 – 81
x2 – 81
First Term Coefficient: First Term Variable: Second Term: 1
= 1 x2
= x 81
= 9
(x + 9)(x – 9)

4. Example 2b: Find the roots
(x + 9)(x – 9) = 0
x + 9 = 0
x – 9 = 0 -9
+ 9
_________ -9
+ 9
_________
x = - 9
x = 9

5. Factor the polynomial: x2 – 144
Guided Practice 4a
Factor the polynomial: x2 – 144
A] (x + 12)(x – 12)
B] (x + 72)(x – 72)
C] (x + 36)(x – 36)
D] Prime
First Term Coefficient: First Term Variable: Second Term:

6. Find the roots: (x + 12)(x – 12) = 0
Guided Practice 4b
Find the roots: (x + 12)(x – 12) = 0
A] x = 12 and -12
B] x = 12
C] x = -12
D] Prime

7. Factor the polynomial : x2 – 49
Guided Practice 5a
Factor the polynomial : x2 – 49
A] (x + 49)(x – 49)
B] (x )(x – 24.5)
C] (x + 7)(x – 7)
D] Prime
First Term Coefficient: First Term Variable: Second Term:

8. Find the roots: (x + 7)(x – 7) = 0
Guided Practice 5b
Find the roots: (x + 7)(x – 7) = 0
A] x = 7
B] x = -7
C] x = 7 and -7
D] Prime

9. Factor the polynomial: x2 + 121
Guided Practice 6
Factor the polynomial: x
A] (x + 121)(x – 121)
B] (x )(x – 60.5)
C] (x + 11)(x – 11)
D] Prime

10. Example 2: Factor 2x2 - 72
2x2 – 72
First Term: Second Term:
2 • 1 • x • x
2 • 36
2(x2 – 36)
= 1
First Term Coefficient: First Term Variable: Second Term: 1 x2
= x 36
= 6
2(x + 6)(x – 6)

11. Factor the polynomial: 4x2 – 121
Guided Practice 7
Factor the polynomial: 4x2 – 121
GCF: First Term Coefficient: First Term Variable: Second Term:
A] (2x + 11)(2x – 11)
B] 4(x2 – 30.25)
C] (2x )(2x – 60.5)
D] Prime

12. Find the roots: (2x + 11)(2x – 11) = 0
Guided Practice 7
Find the roots: (2x + 11)(2x – 11) = 0
A] x = 5.5
B] x = -5.5
C] x = 5.5 and -5.5
D] Prime

13. Factor the polynomial: 3x2 – 507
Guided Practice 8a
Factor the polynomial: 3x2 – 507
GCF: First Term Coefficient: First Term Variable: Second Term:
A] 3(x )
B] 3(x + 13)(x – 13)
C] 3(x2 – 169)
D] Prime

14. Find the roots: 3(x + 13)(x – 13) = 0
Guided Practice 8a
Find the roots: 3(x + 13)(x – 13) = 0
A] x = 169
B] x = 13 and -13
C] x = 13
D] Prime

15. Factor the polynomial: 4x2 + 25
Guided Practice 9
Factor the polynomial: 4x2 + 25
A] 4(x )
B] (2x + 5)(2x – 5)
C] 2(2x )(2x – 12.5)
D] Prime