1. Factoring with GCF and DOS

2. Table of Contents
46: Warm-Up, Guided Practice, Reflection
47: How Do I Factor Quadratics Using Greatest Common Factor (GCF) and Difference of Squares (DOS)?

3. Warm-Up List all the square from 1 to 20 # Sq 1 8 15 2 9 16 3 10 17 411 18 5 12 19 6 13 20 7 14 1 64
225 4 81
256 9
100
289 16
121
324 25
144
361 36
169
400 49
196

4. Padlet Warm Up List what you know about the graphs/equations of:
F(x) = A(x – r)(x – s) G(x) = Ax2 + Bx + C
Period 4 Period 6

5. Learning Intention/Success Criteria
LI: We are learning to factor quadratics using difference of squares (DOS) and greatest common factor (GCF) 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

6. EQ: How Do I Factor Using Difference of Squares and Greatest Common Factor?
5/19/2019

7. Teach Me How To Factor Video

8. Greatest Common Factor (GCF)
The largest term that divides evenly into a given polynomial
Perfect Square
Any number that is a square of a rational number
Prime
A positive integer or term which has only the number 1 and itself as factors

9. Difference of Squares
Two perfect squares separated by a subtraction sign
a2 – b2
= (a + b)(a – b)

10. Example 1: Factor the polynomial using GCF
10x2 + 5x
First Term: Second Term:
5 • 2 • x • x
5 • 1 • x 5x
(2x + 1)

11. Factor the polynomial using GCF: 7x – 21
Guided Practice 1
Factor the polynomial using GCF: 7x – 21
A] Prime
B] 7(x – 3)
C] 7(x – 21)
D] 3(7x – 7)

12. Factor the polynomial using GCF: 16x3 + 24x2 – 8x
Guided Practice 2
Factor the polynomial using GCF: 16x3 + 24x2 – 8x
A] 4(4x3 + 6x2 – 2x)
B] 4x(4x2 + 6x – 2)
C] 8x(2x2 + 3x – 1)
D] 2x(8x2 + 12x – 4)

13. Factor the polynomial using GCF: 7x3 – 5z2 + 3x2z2
Guided Practice 3
Factor the polynomial using GCF: 7x3 – 5z2 + 3x2z2
A] x2z2(7x – 5 + 3)
B] 5z2(7x3 – 1 + 3x2)
C] 7x2(x – 5z2 + 3z2)
D] Prime

14. Predict
What is the difference between the words “factor” and “solve”?

15. Example 2a: Factor x2 – 81
x2 – 81
First Term Coefficient: First Term Variable: Second Term: 1
= 1 x2
= x 81
= 9
(x + 9)(x – 9)

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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Predict
Do you think you can use GCF and Difference of Squares at the same time? Why or why not?

23. Example 3: 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)

24. Factor the polynomial: 4x2 – 121
Guided Practice 7
Factor the polynomial: 4x2 – 121
A] (2x + 11)(2x – 11)
B] 4(x2 – 30.25)
C] (2x )(2x – 60.5)
D] Prime

25. 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

26. Factor the polynomial: 3x2 – 507
Guided Practice 8a
Factor the polynomial: 3x2 – 507
A] 3(x )
B] 3(x + 13)(x – 13)
C] 3(x2 – 169)
D] Prime

27. 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

28. 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

29. Predict
Once a polynomial is factored and solved, what does your answer show you?