4-4 Factoring Quadratic Expressions
FOIL - finding the product, given the factors
Factoring - finding the factors, given the product
(Opposites of one another!!!)
Think about these questions!
1. What two numbers have a product of 8 and a sum of 6?
2. What two numbers have a product of 56 and a sum of –15?
3. What two numbers have a product of –24 and a sum of 5?
**Remember these types of questions!!
Factoring 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 (a trinomial), when 𝑎 = ±1.
Steps: 1. Start: (x )(x )
2. Look at the sign of the last term.
3. If the sign is positive:
a. Signs in both parentheses are the same!
b. use the sign from the second term!
4. If the sign is negative:
a. signs in the parentheses are different!
5. Ask yourself: What two numbers have a product of c and a sum of b?
6. You can check your answer by using the FOIL method.
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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Example 1: Factor each trinomial.
a. 𝑥 2 + 5𝑥 + 4
b. 𝑥 2 + 7𝑥 + 12
c. 𝑎2 + 8𝑎 − 20
d. 𝑦 2 − 8𝑦 + 12
e. 𝑥 2 − 3𝑥 − 18
f. 𝑑 2 − 27𝑑 − 90
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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Example 2: Factor each trinomial. Factor out a -1 first!!!!
a. −𝑥 2 − 10𝑥 − 25
b. −𝑧 2 + 13𝑧 − 12
c. −𝑥 2 + 14𝑥 + 32
d. −𝑥 2 + 13𝑥 − 12
e. −𝑎2 + 5𝑎 − 6
f. −𝑏 2 − 7𝑏 − 10
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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Example 3: Factor each expression.
a. 6𝑛2 + 9𝑛
b. 4𝑥 2 + 20𝑥 − 56
c. 7𝑛2 − 21
d. 9𝑥 2 + 9𝑥 − 18
e. 4𝑥 2 + 8𝑥 + 12
f. 5𝑥 2 − 25𝑥
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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Example 4: Factoring 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 (a trinomial), when |𝑎| ≠ 1.
a. 2𝑥 2 + 11𝑥 + 12
b. 4𝑥 2 − 4𝑥 − 3
c. 4𝑥 2 + 7𝑥 + 3
d. 2𝑥 2 − 7𝑥 + 6
e. 2𝑥 2 + 5𝑥 − 12
f. 6𝑥 2 + 5𝑥 − 21
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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Two Special Cases
Perfect Square Trinomials:
𝑎𝑥 2 + 2𝑎𝑏 + 𝑏 2 = (𝑎 + 𝑏)2 and 𝑎𝑥 2 − 2𝑎𝑏 + 𝑏 2 = (𝑎 − 𝑏)2
Difference of Two Squares
𝑎2 − 𝑏 2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
Example 5: Factor each expression.
a. 4𝑥 2 − 24𝑥 + 36
b. 25𝑥 2 − 49
c. 64𝑥 2 − 16𝑥 + 1
d. 16𝑥 2 − 81
e. 81𝑥 2 − 100
f. 𝑥 2 − 12𝑥 + 36
Homework: pp. 229 – 230 => 1; 2; 9 – 25 (day 1)
p. 234 => 1 – 4; 7 – 23 (day 2)
Algebra 2: Lesson 4-4 Factoring Quadratic Expressions
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