Hyunbok Huh

Warm Up 1. Arrange 12 unit squares into a rectangle, and then look at possible lengths and widths. You can have multiple pairs of possible lengths and widths. That is to say, draw any rectangle containing 12 unit squares. And measure the length and the width in the rectangle. 2. What is the relationship between 12 and those pairs of possible lengths and widths. unit square Write down your name and date: This will be included in the next Portfolio.

Connect between factors and the dimensions of a rectangle. Understand the meaning of factoring in the number and polynomials. Factor any trinomial in quadratic function and model them. Connect factoring polynomials with zeros of the polynomials. The Objective

To factor means to rewrite an expression as a product. What is a product? Multiplication? A product(multiplication) is an area. How? What Is Factoring? Note1.

What is 23 x 14? It is the area of 23 x 14. How do you find out the area? This is a unit square. How many unit squares are in the rectangle? Note2.

To factor means to rewrite an expression as a product. What are factors of 6? Why are 1,2,3,and6 factors of 6? Prove it. First, 6 is a product of 1&6 and 2&3. This is the way to find out the area of the rectangle. If you multiply two factors(the length and width), you find out the area. What Are Factors of 6? Why? Note3.

Does This Work for Polynomials?

To factor means to rewrite an expression as a product. What Is Factoring in Polynomials? Note4.

Factoring with Algebra Tiles

What’s the Area below? Answer for each of the following. “What’s the length and the width? What’s the area?” 1) 2) 3) 4) White Board!!!

What’s the Area below? White Board!!!

What Model Is (x+1)(3x+3)? White Board!!!

What Model Is (2x+1)(2x+2)? White Board!!!

(i) Select the tiles which represent the product, i.e., area. (ii) Make a rectangular array of the tiles by placing large square tiles in the upper left corner and the unit (1) tiles in the lower right corner. (iii) Read the dimensions, i.e., factors, of the completed rectangle. Factoring with Algebra Tiles Note5.

Activity I: Construct Rectangle to Factor out with the Algebra Tiles CW1. Write down your name and date: This will be included in the next Portfolio.

Sample Answer Key

Activity II: Factoring with Algebra Tiles CW2. Write down your name and date: This will be included in the next Portfolio.

Activity II: Factoring with Algebra Tiles CW3. Write down your name and date: This will be included in the next Portfolio.

Activity II: Factoring with Algebra Tiles CW4. Write down your name and date: This will be included in the next Portfolio.

What if we cannot factor out the polynomial with that method… For example, can we factor x² + 8x + 3? Yes or No? Use the quadratic formula to find out the real roots. Why do we practice factoring the polynomials a lot? What can we do with the factor of the trinomial? By factoring, we can find out the real roots, which is x-intercept. This is to say, the real roots are zeros of the polynomial. The Further to Think… Note 6.

Polynomial: Bounds on Zero What are -1, 1, and 2 graphically? f(x)= f(1)=? f(-1)=? f(2)=? Therefore, -1, 1, and 2 are called zeroes of the polynomials, which are x-intercepts of the function. The curve of the graph bounds on these points. Note 7.

Reflection Note 8.

Other Factoring Factor out a monomial Factor by grouping

Other Factoring Skills The ratio of the last coefficient and the leading coefficient The cross product… The quadratic formula…

Question: What did you learn from today’s class?

Connection…

Summative Assessment (from SAT practice problems) Write down your name and date: This will be collected and graded as well as included in the next Portfolio.

Homework Name: Write down your name and date: This will be collected and graded as well as included in the next Portfolio.