Section 8.7- Factoring Special Cases
Essential Question: How can we connect factoring and FOIL?
Do Now:
Part 1:
Consider the following trinomials.
a. 𝑥 2 − 81
b. 𝑥 2 − 16
c. 𝑥 2 − 25
1) What are the values for A, B, and C?
Equation a:
A= ________
B= __________
C= _________
Equation b:
A= ________
B= __________
C= _________
Equation c:
A= ________
B= __________
C= _________
2) Play the detective game for all three equations. What pattern do you notice about the
factors you chose?
Part 2:
Factor the following trinomials.
a. 𝑥 2 − 8𝑥 + 16
b. 4𝑛2 − 12𝑛 + 9
i. What do you notice about the answer?
ii. What do you notice about the first and last terms of the trinomial?
iii. How is the middle term related to the first and last terms?
Example 1: Factoring a Perfect-Square Trinomial
What is the factored form of each expression?
a. 𝑥 2 − 14𝑥 + 49
b. 4𝑟 2 + 36𝑟 + 81
c. 𝑥 2 + 6𝑥 + 9
d. 25𝑧 2 − 40𝑧 + 16
Key Concept: Factoring a Difference of Two Squares
Algebraic Formula
Notes
For all real numbers a and b:
Example 2: Factoring a Difference of Two Squares
What is the factored form of each expression?
a. 𝑧 2 − 9
b. 16𝑥 2 − 81
c. 𝑣 2 − 100
d. 25𝑑 2 − 64
Example 3: Factoring out a Common Factor
What is the factored form of each expression?
a. 24𝑔2 − 6
b. 12𝑥 2 + 12𝑥 + 3
Example 4: Factoring to Find a Length
You are building a square patio. The area of the patio is 16𝑥 2 − 72𝑥 + 81. What is the
length of one side of the patio?
Group Work:
Complete ALL Problems.
Factor the expressions for questions 1-3.
1) 𝑦 2 − 16𝑦 + 64
2) 9ℎ2 − 64
3) The area of a square is
36𝑤 2 + 60𝑤 + 25. What is the side length
of a square? Use factoring.
4) 80𝑔2 − 45
5) Explain how to determine whether a binomial is a difference of two squares.
HW: p. 526-527 #9-37 every other odd, 39, 40