NAME LIST DAVID 2x²-3X-9 ADELA ALICE VIVIAN Ms. PROFESSIOR JIM Mr. PROFESSIOR

When Alice escape from the Evil David, however she doesn’t aware that a more frightening trip is waiting for her. THE POLYNOMIAL WORLD

2X ²-3X-9

2X²-3X-9’s PLAN Use the secret weapon Algebra Tiles to slow down Alice’s movement Try to force Alice give up by using the strategy of factoring and multiplying polynomials The demonstration of the Distributive Method to prevent Alice from escaping Trump the Method of Decomposition to wipe out Alice 2X ²-3X-9

Round 1 Algebra Tiles

Factor the binomial 6c + 4c² using algebra tiles and by finding the GCF Solution: 1. Find the GCF 2.Use Algebra Tiles 3.Reach the conclusion Solution: 2c(2c+3) SO EASY

EASY?! Ha, How about this one! Factor the trinomial 5 – 10z – 5z². Tips: When a polynomial has negative terms or 3 different terms (a trinomial), we cannot remove a common factor by arranging the tiles as a rectangle. Instead, we can sometimes arrange the tiles into equal groups. SO HAPP Y

Solution: 1. Find the GCF 2.Use Algebra Tiles 3.Make group of Tiles 4.Reach the conclusion THX, PRO. THX, PRO.

2X ²-3X-9

Round 2 Multiply polynomials

Multiplying with Algebra Tiles and Rectangle Diagrams It’s time to talk about the business. Name the solution to (X+3)(X+5) HELP

Multiplying with Algebra Tiles and Rectangle Diagrams Step 1: Draw two dimensions, write polynomials beside them Step 2: Represent the two polynomials Step 3: Draw the tiles Step 4: Color the tiles Step 5: Get the result

x+ 3 x+ 5 X²3X 5X15 SOLUTION: X²+8X+15 SOLUTION: X²+8X+15

2X ²-3X-9

Round 3 Distributive Method 2X ²-3X-9

Distributive Method Factor the trinomial z 2 – 12z + 35 Solution: 1. Find (a)+ (b), and (a)*(b) 2. Then find two numbers that add to (a)+ (b), multiply to (a)*(b)

Distributive Method So a=0,b=-12 then, (a)+ (b)=- 12 (a) (b)=35, so the possible answer is 5 and 7 The solution : (z-5)(z-7)

Multiply: (-3f 2 + 3f – 2)(4f 2 – f – 6) Distributive Method Solution: multiply each term in the trinomial by each term in the binomial. I need Jack to help!

Distributive Method The distributive property can be used to perform any polynomial multiplication. Each term of one polynomial must be multiplied by each term of the other polynomial. I can do it!

2X ²-3X-9

Round 4 Method of Decomposition

Alice, I’ll get you! Factor 6x² – 21x + 9 ? ?

Step 1 : Multiply (a) (c) to find a product used to decompose (b) Step 2 : Find two factors of your product that when added together equal (b) Step 3 : Break apart, or decompose (b) into two x terms using the two factors just found Step 4 : Group the first two terms and the last two terms and remove the GCF Step 5 : Put the common factors into one set of brackets and multiply by one of the identical binomials

Here, a = 6, b = -21, c = 9. Step 1) Multiply (a) and (c) to find a product that will be used to break apart (b), or “decompose” (b). So, (a)(c) = (6)(9) = 54

Step 2) Now find any two factors of 54 that when added together, equal (b), or -21. *Remember that negative numbers may be factors too. In this case, two factors that add to -21 are -9and -1

Step 3) Now, break apart (decompose) the middle term, (b), into two x terms, using the two factors just found (-9 and -1). So, 6x² – 21x + 9 now becomes 6X ² - 9x -x + 9 *The order of terms doesn’t matter

Step 4) Find the common factor between the first two terms （ 6X²- 9x ） as well as the last two terms （ -x + 9 ） and factor them out. For this example, the common factor of the first two terms is 3x, and the common factor of the last two terms is 1

Step 5) Put the two factored out terms into one pair of brackets (3X+1), and take one of the identical binomials (x+ 5) and rewrite the expression like this: 3(2x – 1)(x – 3) You have now factored the polynomial. I’m safe! God!

2X ²-3X-9

ALICE IS GRABED INTO THE EVIL ROOM

With the help of 10B, Alice escaped from the Polynomial World. And our poor David fail Mr. Heard’ s test only because he is always day-dreaming about the Alice’s wonderland while having math lessons. Yep, it’s only a dream.