Emily and Zach have two different polynomials to multiply:

Polynomial product A:
(4x2 – 4x)(x2 – 4) Polynomial product B:
(x2 + x – 2)(4x2 – 8x)
They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

1. Complete the table to summarize each student's conjecture about how to solve the problem. (2 points: 1 point for each row of the chart)

Classmate Conjecture
Emily



Zach



Evaluating the Conjectures

Who do you think is correct? (1 point)




Analyzing the Data

Table Method:

2. Use the table to find the products of the two polynomials. Write your answer in descending order. (4 points: 2 points for each product)

A) (4x2 – 4x)(x2 – 4)

4x2 –4x
x2
–4










B) (x2 + x – 2)(4x2 – 8x)

____ ____ ____
____
____
____










3. Are the two products the same when you multiply them with the table method? (1 point)






Multiplying Using the Distributive Property:

4. Multiply the two polynomials using the distributive property. (4 points: 2 points for each product)

A) (4x2 – 4x)(x2 – 4)











B) (x2 + x – 2)(4x2 – 8x)











5. Are the two products the same when you multiply them horizontally? (1 point)






Multiplying Vertically:

6. Find the product for both sets of polynomials below by multiplying vertically. (4 points: 2 points for each product)
A)











B)











7. Are the two products the same when you multiply them vertically? (1 point)






Making a Decision:

8. Who was right, Emily or Zach? Are the products the same with the three different methods of multiplication? (1 point)






9. Which of these three methods is your preferred method for multiplying polynomials? Why? (1 point)