1. Algebra – Ch. 9.8B Factoring Out GCF & Solving
Mr. Deyo
a2 + 2ab + b2

2. Learning Target
By the end of the period, I will solve trinomial products by first factoring out negative leading coefficients and greatest common factors.
I will demonstrate this by completing Four-Square notes and by solving problems in a pair/group activity.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 9.8 pg ) Section ______
TxtBk. Problems #25-39 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Vocabulary Perfect Squares Perfect Square Trinomial (2 examples)
Difference of Two Perfect Squares
Factor Completely (GCF)

6. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

7. Hax2+Hbx+Hc = H(ax2-bx-c)
Notes:
Negative Leading Coefficient
-ax2 + bx + c = -1(ax2 - bx - c)
Factor Out GCF First! (If possible)
Hax2+Hbx+Hc = H(ax2-bx-c)

8. Storm Check (Think, Write, Discuss, Report)
What should you do if you see a negative leading coefficient in a trinomial? When I see a negative leading coefficient in a trinomial, I should ________________________ _______________________________________.

9. 12n -n2 + 36 - Example 2 Factor the polynomial. a.
Factor Negative Leading Coefficient Problem A
Factor the polynomial.
12n
-n2 a. + 36 -

10. 12n -n2 + 36 - = -1( n2 - 12n + 36) -1( )2 6 n – = = -1( ( ) 2 n2 – 62
Example 2
Factor Negative Leading Coefficient Problem A
Factor the polynomial.
12n
-n2 a. + 36 -
= -1( n2 -
12n +
36)
Write as
= -1( ( ) 2 n2 – 62 + 6 n •
2ab a2 b2
-1( )2 6 n –
Perfect square trinomial pattern =

11. 4st -4s2 t2 - 12x -9x2 + 4 - Example 2 Factor the polynomial. b. c.
Factor Negative Leading Coefficient Problems B
Factor the polynomial.
12x
-9x2 b. + 4 -
4st
-4s2 c. t2 -

12. 4st 4s2 t2 + 12x -9x2 + 4 - 12x -1(9x2 – 4) + = -1[ ( ) 2 – 22 + 3x •
Example 2
Factor Negative Leading Coefficient Problems B
Factor the polynomial.
12x
-9x2 b. + 4 -
12x
-1(9x2 = – 4) +
Write as
= -1[ ( ) 2 – 22 + 3x •
2ab a2 b2 )2 ] ( )2 2 3x –
Perfect square trinomial pattern
= - 1
4st
4s2 c. t2 +
Write as = ( ) 2 + t2 t 2s •
2ab a2 b2 )2 ( )2 t 2s +
Perfect square trinomial pattern =

13. Guided Practice
Problems “A”
Factor the polynomial COMPLETELY (Look for GCF first). 1.
24t
4t2 – 36 +

14. 1. 24t 4t2 – 36 + ( )2 3 t – 4 Guided Practice
Problems “A”
Factor the polynomial COMPLETELY (Look for GCF first). 1.
24t
4t2 – 36 +
ANSWER ( )2 3 t – 4

15. 1. 2. 20y 2y2 – 50 + 6xy 3x2 3y2 + Guided Practice
Problems “B”
Factor the polynomial COMPLETELY (Look for GCF first). 1.
20y
2y2 – 50 + 2.
6xy
3x2
3y2 +

16. Guided Practice
Problems “B”
Factor the polynomial COMPLETELY (Look for GCF first). 1.
20y
2y2 – 50 +
ANSWER ( )2 5 y – 2 2.
6xy
3x2
3y2 +
ANSWER ( )2 y x + 3

17. Storm Check (Think, Write, Discuss, Report)
When are you able to factor out a GCF from a trinomial? You can factor out a GCF from a trinomial when _______________________________________ _______________________________________.

18. Learning Target
By the end of the period, I will solve trinomial products by first factoring out negative leading coefficients and greatest common factors.
I will demonstrate this by completing Four-Square notes and by solving problems in a pair/group activity.

19. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section ______ 3) Section ______
WkBk. Problems_________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

20. Vocabulary Perfect Squares Perfect Square Trinomial (2 examples)
Difference of Two Perfect Squares
Factor Completely (GCF)

21. Factored Form (x + f) (x + g) = 0
Zero Product Property
Standard Form x bx c = 0
Factored Form (x + f) (x + g) = 0
Solve for Roots (x + f) = 0 (x + g) = 0
- f - f g g
Roots (Solutions) x = - f x = - g
Notes:
Set Factors Equal
To Zero (0)
Zero Product Property
Factors
( ) ( )
(x - f) (x + g) = 0  x = + f, x = - g
Roots
(x - f) (x - g) = 0  x = + f, x = + g
(x + f) (x - g) = 0  x = - f, x = + g

22. Guided Practice
Problem “A”
Solve the equation. 1. =
14w w2 – + 49

23. = 14w w2 – + 49 7 ANSWER Guided Practice Solve the equation. 1.
Problem “A”
Solve the equation. 1. =
14w w2 – + 49
ANSWER 7

24. = 6a a2 + 9 = 81 n2 – Guided Practice Solve the equation. 1.
Problems “B”
Solve the equation. 1. = 6a a2 + 9 2. = 81 n2 –

25. = 6a a2 + 9 3 – 9 – + = 81 n2 – ANSWER ANSWER Guided Practice
Problems “B”
Solve the equation. 1. = 6a a2 + 9
ANSWER 3 –
ANSWER 9 – + 2. = 81 n2 –

26. Storm Check (Think, Write, Discuss, Report)
What does it mean to solve for the roots of a trinomial? To me, solving for the roots of a trinomial means _______________________________________ _______________________________________.

27. Vocabulary Perfect Squares Perfect Square Trinomial (2 examples)
Difference of Two Perfect Squares
Factor Completely (GCF)

28. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section ______ 3) Section ______
WkBk. Problems_________ Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

29. Learning Target
By the end of the period, I will solve trinomial products by first factoring out negative leading coefficients and greatest common factors.
I will demonstrate this by completing Four-Square notes and by solving problems in a pair/group activity.

30. 64 4y2 – Guided Practice Factor the polynomial COMPLETELY. 1.
Ticket OUT!
Factor the polynomial COMPLETELY. 1. 64
4y2 –

31. 64 4y2 – ( ) 4 + y – Guided Practice Factor the polynomial COMPLETELY.
Ticket OUT!
Factor the polynomial COMPLETELY. 1. 64
4y2 –
ANSWER ( ) 4 + y –