Math Polynomial Area Model Independent Practice

1. Combine like terms and then rewrite each polynomial in standard form.

1. 2x + 7x

2. 2x + 3x2 +7x - 4

3. 3x2 - 2x + 4x + 7

4. 6x3 - 4x + 2 - x

2. Multiply each polynomial. Show your solution steps, and use an area model for at least 4 of the problems.

ANSWER BOX

6x2 -20x + 6

-35x - 56

16x2 - 8x + 1

12x2 + 18x

12x2 + 14x + 2

8x2 + 26x + 6

1.) 6x(2x + 3)

2.) 7(-5x - 8)

3.) (2x + 2)(6x + 1)

4.) (4x + 1)(2x + 6)

5.) (x - 3)(6x - 2)

6.) (4x - 1)2

What is going on with the diagonals?

EXPLORATION

3

a. Multiply (5x + 3)(x + 4) using the area model to the right. Write your answer as a sum below.

b. Multiply the term in box 1 by the term in box 4. Write your answer below.

c. Multiply the term in box 2 by the term in box 3. Write your answer below.

4

a. Multiply (3x + 5)(2x - 1) using the area model to the right. Write your answer as a sum below.

b. Multiply the term in box 1 by the term in box 4. Write your answer below.

c. Multiply the term in box 2 by the term in box 3. Write your answer below.

5. OBSERVATIONS

a. What do you notice about your answers to parts b and c in each of the 2 problems?

b. Do the terms in box 1 and 4 always appear in the sum?

c. What is the greatest common factor of boxes 1 and 2 from problems 1 and 2?