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

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.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 9.8 pg. 576 3) 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

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

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

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

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)

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 ________________________ _______________________________________.

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

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 =

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 -

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 =

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

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

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 +

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

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 _______________________________________ _______________________________________.

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.

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

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

Factored Form (x + f) (x + g) = 0 Zero Product Property Standard Form x2 + 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

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

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

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

= 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 –

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 _______________________________________ _______________________________________.

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

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

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.

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

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