Factoring with Algebra Tiles

Name: ___________________________

Factoring with Algebra Tiles Recall from multiplying with Algebra Tiles - (𝑥 + 1)2 can be pictured as: x

+1

x

+ 1

This is a perfect square polynomial and notice that it looks like a square. It can be written as (𝑥 + 1)2 or 𝑥 2 + 2𝑥 + 1 (because it has an 𝑥 2 tile, two 𝑥 tiles and a 1tile) 1. What two ways can the following be written as? a.

b.

2. Use Algebra Tiles to represent the following perfect squares. Write another expression that represents each. Sketch your answers. a. (𝑥 + 2)2

b. (𝑥 + 4)2

c. (𝑥 − 2)2

d. (𝑥 − 1)2

e. (2𝑥 + 3)2

f.

(2𝑥 − 1)2

3. What do you notice about the x term in each instance?

4. What do you notice about the constant term in each instance?

5. We can do the same thing with rectangles. What two ways can the following be written as? a.

b.

c. (remember −1 ∗ −1 = 1)

d.

6.

Select Algebra Tiles for each term in the following trinomials. Create a square or a rectangle with the tiles. Sketch your answers. Determine the dimensions of each and write down the factors. a. 𝑥 2 + 6𝑥 + 9

b. 4𝑥 2 + 12𝑥 + 9

c. 𝑥 2 − 6𝑥 + 9

d. 𝑥 2 + 3𝑥 + 2

e. 𝑥 2 + 5𝑥 + 6

f.

𝑥 2 + 7𝑥 + 6

g. 𝑥 2 − 1

h. 𝑥 2 − 5𝑥 − 6

i.

2𝑥 2 + 3𝑥 + 1

j.

3𝑥 2 + 5𝑥 + 2