B
College Algebra
Appendix Exam (A.3-A.6)
Name
Directions: You must show all work and reasoning to receive full credit. You work should be neat and
well organized.
Question 0) (1 point) What is the worst gift you ever received? Explain 
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For Questions 1 – 3, answer True or False and explain your reasoning.
1) The polynomial f ( x)  x 2  5 x  7 has no real solutions.
2)  2 x  3  8 x3  27
3

 

3) Synthetic Division can be performed on the following: 4 x 4  5 x3  9 x  10  x 2  1 .
For Questions 4 – 8, factor completely.
4) 𝑥 2 + 𝑥 − 30
7) 3𝑥 3 − 12𝑥 2 − 5𝑥 + 20
5) 8𝑥 2 + 10𝑥 − 3
6) 12𝑎2 − 48𝑏 2
8) 4𝑥 2 (3𝑥 − 1)5 (4𝑥 + 3)3 + 20𝑥 2 (3𝑥 − 1)4 (4𝑥 + 3)4
B
For Questions 9 and 10, simplify and give answer in fully factored, reduced form. State any restrictions
on the variable.
3𝑥2 −6𝑥
( 2
)
6𝑥 −24𝑥+18
5
𝑥+3
9)
+
10)
𝑥2 +4𝑥−12
𝑥+2
2𝑥−3
( 2
)
𝑥 +5𝑥−6
For Questions 11 and 12, perform the indicated polynomial division.
11) synthetic division: (−4𝑥 3 + 5𝑥 2 + 8) ÷ (𝑥 + 3) 12) long division: (8𝑥 3 + 12𝑥 2 + 𝑥 + 10) ÷ (2𝑥 2 + 1)
B
For Questions 13 – 18, analytically solve the equations. Check your solutions on your calculator.
5
10
20
13)
−
= 2
14) 4(3𝑥 + 2)2 − 100 = 0
𝑥+3
𝑥−3
𝑥 −9
15) 2𝑥 2 + 𝑥 = 8
16) 6𝑥 4 − 10𝑥 3 − 4𝑥 2 = 0
17) 3|2 − 4𝑥| − 42 = 0
18) 𝑥 3 + 2𝑥 2 = 9𝑥 + 18
B
For Questions 19 – 21, write the expression in the standard form a  bi .
19) (−3 + 𝑖) − (9 − 6𝑖)
20) (4 − 3𝑖)(−5 − 𝑖)
21)
−3+2𝑖
5−3𝑖
For Questions 22 and 23, solve the equations in the complex number system.
22) 2𝑥 5 + 24𝑥 3 − 128𝑥 = 0
23) 2𝑥 3 + 58𝑥 = 12𝑥 2