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3.3.6 Journal: Breakdown Ahead
Journal
Algebra II Sem 1 (S2881811)
Jason Peridore
Points possible: 20
Date: ____________
Scenario: Factoring Special Cases
Instructions:
View the video found on page 1 of this journal activity.
Using the information provided in the video, answer the questions below.
Show your work for all calculations.
The Students' Conjectures: Teresa and Rico need help with five factoring problems. The first problem is
to factor the following polynomial completely: (x8 – 6561). Complete the table to summarize what you
know about each student’s idea. (2 points: 1 point for each row of the chart)
Classmate
Conjecture
Teresa
Rico
Analyze the conjecture: Without factoring the polynomial, who do you think is right? Is 6561 a perfect
square? (1 point)
Problem 1: Factor the following polynomial completely. (3 points: 2 for partial factoring, 1 for final)
(x8 – 6561)
Problem 2:
Is the following expression true or false? Show your work. (2 points: 1 point for work, 1 for answer)
[x2 + 8x + 16] · [x2 – 8x + 16] = (x2 – 16)2
Rico thinks it's a perfect square trinomial. Teresa says it's the difference of two squares. Who is correct?
(1 point)
Problem 3:
Factor the following polynomial completely. (3 points: 2 points for partial factoring, 1 for final)
–9x2 – 30x – 25
Rico says it's a perfect square trinomial. Teresa says it's not a perfect square trinomial, because the first
term is negative. Who is correct? Why or why not? (1 point)
Problem 4:
Factor the following polynomial completely. (2 points: 1 point for partial factoring, 1 for final)
(y + 4)2 – 2(y + 4) + 1
Is this the product of a perfect square trinomial? Teresa says it is, Rico says it's not. Who is correct? (1
point)
Problem 5:
Factor the following polynomial completely. (2 points: 1 point for partial factoring, 1 for final)
x2n – y2n
Rico says it's a difference of two squares. Teresa says it's not, because of the exponent n. Who is
correct? (1 point)
Making a Decision:Who got the most questions correct, Teresa or Rico? Who's buying the next piece of
pizza? (1 point)
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