Algebra Ch. 9.2 Multiplying Polynomials. Mr. Deyo

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1 Algebra Ch. 9.2 Multiplying Polynomials Mr. Deyo

2 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) 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 9.2 TxtBk. Pg 531 Problems 7, 13, 15, 17 29, 35, 41, 43 Solved and Put in Binder? 3) Section Notes Copied on a blank sheet 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: 1.How are the two images similar? 2.How are they different? 3.How can these two images be related to math?

5 Vocabulary 1) FOIL (First, Outer + Inner, Last) 2) Polynomial 3) Binomial 4) Trinomial

6 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork 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 Word List Friendly Definition Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

7 Daily Warm-Up ExercisesFor For use use with with pages pages xxx xxx Simplify 2 (9a b) 2. Simplify r 2 s rs 3 3) Find the product 3x ( ) 2x 3

8 Daily Warm-Up ExercisesFor For use use with with pages pages xxx xxx Simplify 2 (9a b) ANSWER 18a + 2b 2. Simplify r 2 s rs 3 ANSWER r 3 s 4 3) Find the product 3x ( 2x 3 ). 3x ( 2x 3 ) =3 ( 2 ) x x 3 Regroup factors. = 6x 4 Simplify.

9 Notes: 3 Methods of Multiplying Polynomials: *1) # by # Table 2) FOIL (x + 2) (x + 2) (a + b) (c + d) 3) Vertical Multiplication x 2 + 4x + 4 ac + ad + bc + bd * Preferred Method

10 Example 3 Multiply polynomials using a table Problem A Find the product ( x 4( ) 3x +2).

11 Example 3 Multiply polynomials using a table Problem A Find the product ( x 4( ) 3x +2). SOLUTION STEP 1 Write subtraction as addition: ( x 4( ) 3x +2 ) = [ x +( 4) ]( 3x +2) STEP 2 Make a table of products. 3x 2 3x 2 x 3x 2 x 3x 2 2x x 8 ANSWER The product is 3x 2 + 2x 12x 8, or 3x 2 10x 8.

12 Guided Practice Problems B Find the product. 1. 5x 3 ( 3x) 2. x ( 7x 2 +4) 3. ( 4n 1( ) n +5)

13 Guided Practice Problems B Find the product. 1. 5x 3 ( 3x) ANSWER 15x 4 2. x ( 7x 2 +4) ANSWER 7x 3 +4x 3. ( 4n 1( ) n +5) ANSWER 4n 2 +19n 5

14 Storm Check (Think, Write, Discuss, Report) If multiplying polynomials, how would you modify the table for a binomial by a trinomial (2 x 3) or a trinomial by a trinomial (3 x 3)? For a binomial multiplied by a trinomial (2 x 3), I. For a trinomial multiplied by a trinomial (3 x 3), I.

15 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) Square notes and by solving problems in a pair/group activity.

16 Home Work 1 2 3: 1) Class 4 Square Notes Put In Binder? 2) Section 3) Section TxtBk. Problems Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

17 Example 4 Find the product +b 2 Multiply polynomials vertically or by using a table (Problem A) +3b -4 ( b 2 +6b 7) ( 3b 4). +6b -7

18 Example 4 Find the product Multiply polynomials vertically or by using a table (Problem A Check) +3b -4 ( b 2 +6b 7) ( 3b 4). +b 2 +6b 3b 3 4b 2 +18b 2 24b -7 21b +28 3b b 2 45b+28

19 Example 4 Multiply polynomials vertically Find the product ( b 2 +6b 7) ( 3b 4). SOLUTION STEP 1 Multiply by 4. b 2 +6b 7 STEP 2 Multiply by 3b. b 2 +6b 7 3b 4 3b 4 4b 2 24b +28 4b 2 24b +28 3b b 2 21b

20 Example 4 Multiply polynomials vertically STEP 3 Add products. b 2 +6b 7 3b 4 4b 2 24b +28 3b b 2 21b 3b b 2 45b +28

21 Example 5 Multiply polynomials Problem B Find the product ( 2x 2 +5x 1( ) 4x 3). +4x -3 +2x 2 +6x -1

22 Example 5 Multiply polynomials Problem B Find the product ( 2x 2 +5x 1( ) 4x 3). +4x -3 +2x 2 +8x 3 6x 2 +6x +24x 2 18x -1 4x +3 = 8x 3 +14x 2 19x +3

23 Example 6 Multiply binomials using the FOIL pattern Find the product ( 3a +4) ( a 2). ( 3a +4) ( a 2) = ( 3a )( a ) + ( 3a )( 2) + ( 4) ( a ) + ( 4) ( 2) =3a 2 + ( 6a) + 4a + ( 8) =3a 2 2a 8 Write products of terms. Multiply. Combine like terms.

24 Guided Practice for Examples 4, 5, and 6 Find the product. 4. ( x 2 +2x +1( ) x +2) ANSWER x 3 +4x 2 +5x ( 3y 2 y +5 )( 2y 3) ANSWER 6y 3 11y 2 +13y ( 4b 5( ) b 2) ANSWER 4b 2 13b +10

25 Guided Practice for Examples 4, 5, and 6 Find the product. 4. ( x 2 +2x +1( ) x +2) 6. ( 4b 5( ) b 2) 5. ( 3y 2 y +5 )( 2y 3)

26 Storm Check (Think, Write, Discuss, Report) Of the three methods to multiply polynomials, which do you prefer to use? Why? I prefer to use the method because.

27 Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication. I will demonstrate this by completing Four(4) Square notes and by solving problems in a pair/group activity.

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

29 Vocabulary Review 1) FOIL (First, Outer + Inner, Last) 2) Polynomial 3) Binomial 4) Trinomial

30 Example 7 Solve a multi-step problem SKATEBOARDING You are designing a rectangular skateboard park on a lot that is on the corner of a city block. The park will be bordered by a walkway along two sides. The dimensions of the lot and the walkway are shown in the diagram. Write a polynomial that represents the area of the skateboard park.

31 Example 7 Solve a multi-step problem SOLUTION a. Write a polynomial using the formula for the area of a rectangle. The park s length is the lot s length minus the width of the sidewalk, or 45 x. Similarly, the park s width is 33 x.

32 Example 7 Solve a multi-step problem Area = length width Formula for area of a rectangle =( 45 x )( 33 x) Substitute for length and width. = x 33x + x 2 Multiply binomials. = x + x 2 Combine like terms. b. What is the area of the park if the walkway is 3 feet wide? (45-3) (33-3) (42)(30) 1260 square feet

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