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Factoring Polynomials:
Classwork/Practice Packet
Lesson 1:
pg. 3
Lesson 2:
Using the Greatest Common Factor and the Distributive
Property to Factor Polynomials
Solving Literal Equations by Factoring
Lesson 3:
Finding Factors, Sums, and Differences
pg. 6
Lesson 4:
Factoring Trinomials of the Form 𝑥 2 + 𝑏𝑥 + 𝑐
pg. 7
Lesson 5:
Factoring Binomials that are the Difference of Two Perfect
Squares
WHAT AM I? HOW DO I FACTOR?
More Review
Prime Polynomials
pg. 9
Lesson 7:
Factoring Expressions Completely
Factoring Expressions with Higher Powers
pg. 14
Lesson 8:
Factoring Trinomials of the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where 𝑎 ≠ 1
pg. 15
Review
More Practice
Factoring with Pizzazz worksheets
pg. 16-30
Review:
Lesson 6:
pg. 5
pg. 10
pg. 11
pg. 13
Page 2
Page 3
Lesson 1:
Factoring using the Greatest Common Factor
Factor each expression by factoring out the GCF.
1.)
𝑥𝑦 − 𝑥𝑧
2.)
4.)
27𝑦 3 + 18𝑦 2
5.)
7.)
2𝑥 2 𝑦 − 2𝑥𝑦
8.)
9𝑥 2 − 3𝑥
3.)
21𝑏 − 15𝑎
12𝑥 2 − 16𝑥
6.)
28𝑥 5 − 7𝑥 2
8𝑚3 + 16𝑚2 𝑛
9.)
4𝑏 3 + 2𝑏 2 + 8𝑏
Page 4
Factor each expression by factoring out the GCF.
10.) 𝑥(𝑥 + 2) + 7(𝑥 + 2)
11.) 2𝑥(𝑥 + 4) − 3(𝑥 + 4)
12.) 4𝑥(𝑥 − 3𝑦) − 2(𝑥 − 3𝑦)
13.) 5𝑎(2𝑎 − 3𝑏) + 6(2𝑎 − 3𝑏)
14.) (3𝑛 + 1)(4𝑛 + 1) + (𝑛 + 2)(4𝑛 + 1)
15.) (2𝑥 + 5)(𝑥 − 4) − (𝑥 − 4)(5𝑥 + 2)
Page 5
Lesson 2:
Solving Literal Equations
Solve each equation for the given variable.
1.)
Solve for 𝑎: 𝑎𝑥 + 𝑧 = 𝑎𝑤 − 𝑦
2.)
Solve for 𝑐:
𝑆 = 2𝑎𝑏 + 2𝑏𝑐 + 2𝑎𝑐
3.)
Solve for π: 𝑉 = 2𝜋𝑟 2 + 2𝜋𝑟ℎ
4.)
Solve for 𝑡: 𝐴  𝑝  𝑝𝑟𝑡
5.)
If 9𝑥 + 2𝑎  𝑎𝑐 − 𝑏𝑥, then 𝑥 equals
6.)
If 𝑥 + 𝑦  𝑛𝑥 + 𝑧, then 𝑥 is equal to
Page 6
Lesson 3:
Finding Factors, Sums, and Differences
Find two factors whose product and sum is as indicated:
Product
Sum
−6
Factors
Product
Sum
1
−56
1
36
−13
35
12
−16
−6
−32
−3
−4
0
−24
5
−33
8
−42
−1
20
9
6
−5
6
−7
14
−9
81
−18
1
2
−12
−1
−6
5
55
−56
−121
0
48
14
−32
14
100
25
25
−24
−49
0
−40
6
7
8
−52
−9
3
-4
−6
−5
−28
3
1
−2
21
10
54
−15
56
15
16
10
−22
9
−27
6
Factors
Page 7
Lesson 4:
Factoring Trinomials of the form 𝒙𝟐 + 𝒃𝒙 + 𝒄
Factor each trinomial.
1. ) 𝑥 2 − 6𝑥 − 16
2.) 𝑥 2 + 14𝑥 + 24
3.) 𝑥 2 − 8𝑥 + 7
4.) 𝑥 2 − 8𝑥 − 9
5.) 𝑥 2 + 4𝑥 − 5
6.) 𝑥 2 + 5𝑥 − 36
7.) 𝑛2 − 15𝑛 + 44
8.) 𝑦 2 + 𝑦 − 110
9.) 𝑥 2 − 16𝑥 + 55
Page 8
10.) 𝑥 2 − 13𝑥 + 12
11.) 𝑥 2 − 10𝑥 + 21
12.) 𝑘 2 − 9𝑘 + 14
13.) 𝑦 2 − 12𝑦 + 11
14.) 𝑥 2 − 7𝑥 + 12
15.) 𝑥 2 − 22𝑥 + 21
16.) 𝑥 2 + 10𝑥𝑦 + 24𝑦 2
17.) 𝑎2 − 13𝑎𝑏 + 42𝑏2
18.) 𝑚2 + 23𝑚𝑛 + 42𝑛2
Page 9
Lesson 5:
Factoring Binomials that are the Difference of Two
Perfect Squares
State whether each polynomial is a difference of two squares. If it is, factor the
expression.
1.)
𝑛2 − 81
2.)
𝑎2 − 121
3.)
𝑛2 + 16
4.)
9𝑥 2 − 144
5.)
2𝑥 2 − 9
6.)
4𝑤 2 − 9
7.)
4𝑛2 − 1
8.)
1 − 16𝑥 2
9.)
𝑥4 − 𝑦2
10.) 9 − 𝑐 2
11.) 𝑛3 − 25
12.) 16𝑥 2 − 6𝑦 2
13.) 49 − 4𝑎2
14.) 𝑎2 𝑏 2 − 𝑐 4
15.) 4𝑥 2 𝑦 2 − 9𝑧 2
Page 10
Review Activity:
What Am I? How do I Factor?
2
2
7𝑥 − 14
𝑏 − 4𝑏 − 45
𝑑 −𝑑−6
𝑚2 − 𝑚
16 − 81𝑦 2
𝑗2 + 11𝑗 + 10
2𝑥 3 + 6𝑥 2
𝑐2 + 𝑐 − 20
25𝑎2 − 256
9𝑥 2 − 4
𝑦2 + 13𝑦 − 48
𝑗2 − 𝑝2
4𝑥 2 − 8𝑥
100 − 𝑘 2
𝑥2 − 8𝑥 + 16
𝑐2 − 1
3𝑥 5 𝑦 + 4𝑥 4 𝑦 − 5𝑥 2 𝑦
3𝑥(2𝑥 − 1) + 4(2𝑥 − 1)
Write the polynomial in the shaded cells in the column that best describes the
method of factoring that should be used. Then factor the polynomial.
Greatest Common
Factor
Polynomial
Factored Form
Polynomial
Factored Form
Polynomial
Factored Form
Polynomial
Factored Form
Polynomial
Factored Form
Polynomial
Factored Form
Difference of Perfect
Squares
Trinomials (no GCF)
Page 11
Review:
Factor each expression completely.
1.) 𝑤 2 + 9𝑤 − 22
2.)
4.)
−4𝑥(𝑥 + 3) + 3𝑥 2 (𝑥 + 3)
7.)
𝑘 2 − 13𝑘 + 42
4𝑥𝑦 2 + 24𝑥 2 𝑦 6
3.) 𝑥 2 − 19𝑥 + 84
6𝑦 2 + 18
6.) 𝑛2 − 19𝑛 + 90
5.)
18.) 144 − 𝑤 2
9.) 𝑚2 − 6𝑚 + 5
10.) 𝑥 2 − 𝑥 − 30
11.) 14𝑐 2 𝑑 + 2𝑐𝑑 2
10.) 𝑧 2 + 8𝑧 + 7
13.) 24𝑥 + 48𝑦
14.) 4(2𝑥 + 7) + 5(2𝑥 + 7) 15.) 𝑎2 − 𝑏 2
Page 12
Factor each expression completely.
16.) 14𝑐 3 − 42𝑐 5 − 49𝑐 4
17.) 15𝑥 5 − 12𝑥 3 + 10𝑥 2
19.) 2𝑥(𝑥 − 5) + 3(𝑥 − 5) + (𝑥 − 5)
18.) 𝑥 8 − 𝑦 4
20.) (𝑥 − 2)(6 − 4𝑥) + (5𝑥 + 4)(𝑥 − 2)
21.) 81 − 100𝑐 2
22.) 6𝑥 2 𝑦 3 + 9𝑥𝑦 4 + 18𝑦 5 23.) 3𝑘 2 + 14𝑘 − 80
24.) 𝑤 2 + 5𝑤 − 6
25.) 6𝑝2 − 29𝑝 + 28
26.) 𝑑 8 − 𝑑 2
27.) 2𝑥 2 − 13𝑥 − 24
28.) 3𝑥 3 − 75𝑥
29.) 𝑥 2 + 17𝑥 + 70
Page 13
Lesson 6:
Prime Polynomials
Factor. If the expression is not able to be factored, write “prime”.
1.)
𝑛2 − 6𝑛 + 5
2.)
𝑥 2 − 13𝑥 + 22
3.)
𝑥 2 + 2𝑥 + 3
4.)
𝑥 2 − 3𝑥 − 4
5.)
𝑛2 − 10𝑛 − 9
6.)
𝑔2 + 7𝑔 − 60
7.)
𝑘 2 − 7𝑘 + 6
8.) 𝑑 2 − 19𝑑 + 90
9.)
𝑎2 + 3𝑎 + 4
10.) 𝑧 2 − 17𝑧 + 72
11.)
𝑥 2 + 7𝑥 + 11
13.) 𝑝2 + 29𝑝 + 30
14.) 𝑥 2 − 2𝑥 − 3
12.) 𝑐 2 + 9𝑐 − 10
15.) 𝑎2 − 8𝑎 − 20
Page 14
Lesson 7:
Factoring Expressions Completely
Factoring Expressions with Higher Powers
Factor completely.
1.)
𝑥 3 + 3𝑥 2 + 2𝑥
2.)
2𝑏 2 − 2
3.)
𝑎3 − 9𝑎2 + 14𝑎
4.)
𝑛4 − 2𝑛3 − 3𝑛2
5.)
−7𝑥 2 + 21𝑥 − 14
6.)
−𝑥 3 + 4𝑥
7.)
36𝑥 2 𝑦 − 64𝑦
8.)
3𝑐𝑑 2 + 12𝑐𝑑 + 12𝑐
9.)
3𝑏 2 + 12𝑏 − 63
10.) 2𝑥 3 − 6𝑥 2 + 4𝑥
11.) −3𝑘 4 + 18𝑘 3 − 24𝑘 2
12.) −8𝑦 2 𝑧 − 40𝑦𝑧 + 48𝑧
Page 15
Lesson 8:
Factoring Trinomials of the form 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄,
where 𝒂 ≠ 𝟏
Factor each trinomial.
1.)
3𝑛2 + 7𝑛 − 20
2.)
7𝑎2 + 48𝑎 + 36
3.)
5𝑣 2 − 41𝑣 − 36
4.)
3𝑏 2 + 22𝑏 − 16
5.)
5𝑛2 − 49𝑛 + 72
6.)
6𝑥 2 − 𝑥 − 12
7.)
4𝑦 2 + 29𝑦 + 30
8.)
4𝑎2 − 16𝑎 − 15
9.)
7𝑛2 + 15𝑛 − 18
Factor completely.
10.) 20𝑎4 𝑏 − 20𝑎3 𝑏 + 5𝑎2 𝑏
11.) 16𝑟 3 + 80𝑟 2 + 100𝑟
12.) 2𝑥 3 𝑦 + 6𝑥 2 𝑦 2 + 4𝑥𝑦 3
13.) 3𝑎3 𝑏 + 15𝑎2 𝑏 2 + 18𝑎𝑏 3
Page 16
Factoring Practice - Algebra with Pizzazz
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