Module 1Algebra

Factoring Trinomial Expressions.

ReviewYou 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

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.

CCSSA-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 OutcomesLearning 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

xx

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INTRODUCTION

Each tile represents an area.x

x Area of large square = x (x) = x2

x Area of rectangle = 1 (x) = x

Area of small square = 1 (1) = 1

1

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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 TilesAlgebra Tiles

Factor: x2 + 5x + 4

What is the length of the rectangle?

What is the width of the rectangle?

Now fill in factors:

X + 4

X + 1

Therefore, the factored form of x2 + 5x + 4 = (x+1)(x+4)

How would you check your answer?

x2 + 5x + 4 = (x+1)(x+4)

(hint: Check review slide.)

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?

Now fill in factors:

X + 2

X + 1

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)

Are you ready?

Working in Partners:Factor: x2 + 7x + 6using Algebra Tiles

When complete, write your final answerin factored form on your wipe board.

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

x2 x x1 1

xx2 x x

►Algebra TilesAlgebra Tiles

2x2 + 5x + 2

Now fill in factors:

X + 2

2X + 1Therefore, the factored form of

2x2 + 5x + 2 = (2x+1)(x+2)

How about…

Factoring 2x2 + 7x + 3

using Algebra Tiles

When complete, write your final answerin factored form on your wipe board.

Lesson Wrap-Up

In this lesson, you learned how to factor trinomials using Algebra Tiles.

You visually saw the connection betweenthe area of a rectangle and its

length and width, each represented byalgebraic expressions (polynomials).

Here’s more:

x2 + 9x + 8 2x2 + 9x + 9

x2 + 8x + 16 2x2 + 10x + 8