Algebra 1 Common Core Student Edition, Grade 8-9

Co n cep t Byt e

Use W ith Lesson 8 -5

Using Models to Fact o r

Common Core State

Standards

Prepares fo r A-SSE.A.2 Use the

structure of an expression to identify ways

to rewrite it.

MP 7

You can som etim es w rite a trinom ial as th e p ro d u c t of two binom ial factors. You can

use algebra tiles to find the factors by arranging all of th e tiles to form a rectangle. The

lengths of the sides of th e rectangle are th e factors of th e trinom ial.

Activity

Write x2 + 7x + 12 as the product of two binomial factors.

Model of polynomial

7x + 12

J J J J J I

Use the tiles to form a rectangle.

First try: Second try:

x + (^6) x+ 5
t
x • 1
There are six | tiles left over.
x + 2
i I J I I J J J
There is one I tile too few.
Third try:
■ x + 4 ■
x + 3
■ JJJJ
mm j j j j
■■ j :j. j j
Correct! There is th e exact n u m b er
of tiles n eeded.
x2 + 7 x + 12 = ( x + 3 ) ( x + 4)
Ex e r c i se s
Use algebra tiles to find binomial factors of each trinomial.

1. x 2 + 4x + 4


2. x2 + 7x + 10


3. x + 5x + 6


4. x 2 + 9x + 14


5. x 2 + lOx + 9


6. x 2 + 8x + 16


7. Reasoning Explain why you can n o t use algebra tiles to re p resen t th e trinom ial
   x2 + 2x + 3 as a rectangle.