Name
Date
Block
Score
UNIT 8 Study Guide: Factoring & Solving Quadratic Equations
Find the greatest common factor.
1.
32 and 64
2.
12 and 21
3.
24x3 and 60x4y2
Factor out the GCF and express your answer as a product.
4.
2x3y2 – 4x2y + 30x2y2
5.
15x2y + 20xy + 25x4y
Factor. (Remember to check for a GCF first!):
6.
x2 – 81
9.
x2 + 10x + 25
13. 9x2 + 30x + 21
17.
x4 + x3 – 12x2
7.
10.
x2 + 3x – 40
14. 8x2 – 13x – 6
18.
4x2 – 16y2
8.
9x4 – 25
x2 – 8x – 9
12.
x2 – 23x + 42
15. 7x2 – 22x + 3
16.
12x2 + 32x – 12
11.
x3 + 3x2 - x - 3
19.
3x3 – 4x2 – 12x + 16
Describe and explain how to correct the error.
20.
Lester and Michael have both factored the polynomial 12x2 + 16x. Lester factored it as 4x(3x + 4), and
Michael factored it as 2x(6x + 8). Who is correct and why?
21.
Jimmy says that 16a4 – 81b8 is factored completely as (4a2 + 9b4)(4a2 - 9b4). Cindy says that he is
incorrect. Who is correct? Explain.
22.
Nick says the factored form of x2 – 3x – 18 = (x + 6)(x – 3). Explain why his solution is incorrect. What
would the trinomial need to be for his solution to be correct?
Find the quotient.
2
23. If 𝑥 ≠ 5, find the quotient of (40𝑛3 − 16𝑛2 + 25𝑛 − 10) and (5𝑛 − 2).
24. Simplify if 𝑝 ≠ −2:
7𝑝2 +9𝑝−10
25. Find the dimensions of the figure below
given the area.
𝑝+2
𝑨 = 𝟖𝒙𝟐 + 𝟏𝟎𝒙 − 𝟑
26. Identify all of the factors of 24𝑛2 − 6𝑛 − 135
when it is factored completely. Circle your answer(s)
below.
𝑛
3
(8𝑛 − 20)
(8𝑛 + 18)
(4𝑛 − 9)
(4𝑛 + 9)
(2𝑛 − 5)
(8𝑛 − 18)
9
27. Identify one of the factors of 36 𝑥 2 − 81 when it is
factored completely. Circle your answer below.
9
9
( 𝑥 + 9)
36
3
( 𝑥 + 81)
6
1
( 𝑥 − 9)
2