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Algebra 8H Final Exam Review #1
Ch.8 – Factoring
8.1 Monomials and Factoring
8.2 Using the Distributive Property
8.3 Factoring Quadratic Equations: 𝑥 2 + 𝑏𝑥 + 𝑐 = 0
8.4 Factoring Quadratic Equations: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
8.5 Factoring Quadratic Equations: Differences of Squares
8.6 Factoring Quadratic Equations: Perfect Square Trinomials
For all chapters, you should know the vocabulary at the end of each chapter and be able to define or describe the
words. I would also suggest you look at your previous quizzes and tests.
To review for mastery of a subject:
1. Complete this packet.
2. Review the quizzes and tests you have already taken and be sure that if you had the same test to take
today, you would get 100%.
3. Read the chapter summaries several times. Write down any ideas that are unclear.
4. Do the Chapter Test for each chapter – These should now be easy.
Lesson 8-1 Monomials and Factoring
Factor each monomial completely.
1) 240𝑚𝑛
2) −231𝑥𝑦 2 𝑧
Find the GCF of each set of monomials.
3) 4𝑥𝑦, −6𝑥
4) −14𝑥𝑦, −12𝑦, −20𝑥
Lesson 8-2 Using the Distributive Property
Use the Distributive Property to factor each polynomial.
1) 10𝑎2 + 40𝑎
2) 2𝑚3 𝑛2 − 16𝑚𝑛2 + 8𝑚𝑛
3) 2𝑎𝑥 + 6𝑥𝑐 + 𝑏𝑎 + 3𝑏𝑐
Solve each equation. Check your solutions.
5) 𝑎(𝑎 − 9) = 0
7) 10𝑥 2 − 20𝑥 = 0
Lesson 8-3 Quadratic Equations: 𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
Factor each trinomial.
1) 𝑥 2 − 9𝑥 + 14
3) 𝑎2 − 9𝑎 − 36
4) 2𝑒 2 𝑔 + 2𝑓𝑔 + 4𝑒 2 ℎ + 4𝑓ℎ
6) (2𝑦 + 6)(𝑦 − 1) = 0
8) 15𝑎2 = 60𝑎
2) 𝑠 2 + 15𝑠 + 36
4) 𝑘 2 − 27𝑘 − 90
Solve each equation. Check your solution.
5) 𝑎2 + 3𝑎 − 4 = 0
7) 𝑥 2 − 57 = 16𝑥
6) 𝑛2 − 9𝑛 = −18
8) −20𝑦 + 19 = −𝑦 2
Lesson 8-4 Quadratic Equations: 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime.
1) 4𝑎2 + 4𝑎 − 63
2) 5𝑥 2 − 17𝑥 + 14
3) 2𝑛2 − 11𝑛 + 13
Solve each equation. Check your solutions.
5) 8𝑡 2 + 32𝑡 + 24 = 0
4) 10𝑥 2 − 20𝑥𝑦 + 10𝑦 2
6) 4𝑥 2 − 4𝑥 − 4 = 4
Lesson 8-5 Quadratic Equations: Differences of Squares
Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.
1) 𝑥 2 − 9
2) 75𝑟 2 − 48
Solve each equation by factoring. Check your solutions.
* Alternative method: Solve by taking the square root of both sides. DO NOT FORGET ABOUT ± *
3) 4𝑥 2 = 16
4) 9𝑛2 − 4 = 0
Lesson 8-6 Quadratic Equations: Perfect Squares
Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.
1) 𝑥 2 + 12𝑥 + 36
2) 𝑛2 − 13𝑛 + 36
3) 4𝑎2 − 20𝑎 + 25
4) 2𝑛2 + 17𝑛 + 21
For each polynomial, if possible. If the polynomial cannot be factored, write prime.
5) 3𝑥 2 − 75
6) 4𝑝2 + 12𝑝𝑟 + 9𝑟 2
7) 6𝑎2 + 72
8) 4𝑐 2 + 2𝑐 − 7
Solve each equation. Check your solutions. Round to the nearest tenth if necessary.
9) 𝑥 2 + 22𝑥 + 121 = 0
10) 𝑐 2 + 10𝑐 + 36 = 11
11) 49𝑑2 = 1
12) (𝑎 − 7)2 = 5