Module 1 Algebra Factoring Trinomial Expressions.

You have learned about solving equations using the Zero Product Rule. Review You have learned about factoring expressions using the Greatest Common Factor (gcf).   You have learned about solving equations using the Zero Product Rule. Bellringer: Solve 2x2 – 10x = 0

We will now learn about how to factor a trinomial such as x2 + 5x + 4. Review (cont’d) You have also learned about using the box method to multiply algebraic expressions: try: (x+1)(x+4). Factor: a number or quantity that when multiplied with another produces a given number or expression. We will now learn about how to factor a trinomial such as x2 + 5x + 4.

CCSS Learning Outcomes A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x2 + 3x + 2 as (x + 1)(x + 2) A-SSE.3 Manipulate expressions using factoring. Learning Outcomes Students will factor expressions using algebra tiles to produce an equivalent form of the expression. Students will relate their findings to area, length and width of rectangles.

INTRODUCTION Algebra tiles can be used to model factoring algebraic expressions . There are three types of tiles: 1. Large square with x as its length and width. 2. Rectangle with x and 1 as its length and its width 3. Small square with 1 as its length and width. x 1 1 x x 1

INTRODUCTION Each tile represents an area. x Area of large square = x (x) = x2 x 1 x Area of rectangle = 1 (x) = x 1 1 Area of small square = 1 (1) = 1

ALGEBRAIC EXPRESSIONS To model x2 + 5x + 4, you need 1 x2 tile, 5 x tiles and 4 one tiles. x2 x x x x x The object is to place these in your grid and form a rectangle. The lengths of each tile must match with the other tiles in its row or column.

Algebra Tiles Factor: x2 + 5x + 4

What is the length of the rectangle? What is the width of the rectangle?

Therefore, the factored form of Now fill in factors: X + 1 X + 4 Therefore, the factored form of x2 + 5x + 4 = (x+1)(x+4)

How would you check your answer? (hint: Check review slide.) x2 + 5x + 4 = (x+1)(x+4)

Factor: x2 + 3x + 2 To model x2 + 3x + 2, you need 1 x2 tile, 3 x tiles and 2 one tiles. x2 x x x

Algebra Tiles Factor: x2 + 3x + 2

What is the length of the rectangle? What is the width of the rectangle?

Therefore, the factored form of Now fill in factors: X + 1 X + 2 Therefore, the factored form of x2 + 3x + 2 = (x+1)(x+2)

How would you check your answer? x2 + 3x + 2 = (x+1)(x+2)

When complete, write your final answer Are you ready? Working in Partners: Factor: x2 + 7x + 6 using Algebra Tiles When complete, write your final answer in factored form on your wipe board.

You need 2 x2 tile, 5 x tiles and 2 one tiles. Let’s factor 2x2 + 5x + 2. You need 2 x2 tile, 5 x tiles and 2 one tiles. x2 x2 x x x x x 1 1

Algebra Tiles 2x2 + 5x + 2

Therefore, the factored form of Now fill in factors: X + 2 2X + 1 Therefore, the factored form of 2x2 + 5x + 2 = (2x+1)(x+2)

When complete, write your final answer How about… Factoring 2x2 + 7x + 3 using Algebra Tiles When complete, write your final answer in factored form on your wipe board.

In this lesson, you learned how to Lesson Wrap-Up In this lesson, you learned how to factor trinomials using Algebra Tiles. You visually saw the connection between the area of a rectangle and its length and width, each represented by algebraic expressions (polynomials).

Here’s more: x2 + 9x + 8 2x2 + 9x + 9 x2 + 8x + 16 2x2 + 10x + 8