CHAPTER EXAM
MATH III
NAME:_____________________
DATE: __________________ SCORE:______________
DIRECTIONS: Choose the best answer from options provided.
1. Use 𝑞(𝑥) = 2𝑥 − 3 and 𝑟(𝑥) = 2𝑥 2 + 3𝑥 − 5. Find 𝑠(𝑥) = 𝑞(𝑥) + 𝑟(𝑥) and 𝑝(𝑥) = 𝑞(𝑥) ∙ 𝑟(𝑥).
a. 𝑠(𝑥) = 2𝑥 2 + 5𝑥 + 8 and 𝑝(𝑥) = 4𝑥 3 + 12𝑥 2 − 19𝑥 + 15
b. 𝑠(𝑥) = 2𝑥 2 + 5𝑥 + 8 and 𝑝(𝑥) = 4𝑥 3 − 𝑥 + 15
c. 𝑠(𝑥) = 2𝑥 2 + 5𝑥 − 8 and 𝑝(𝑥) = 4𝑥 3 − 19𝑥 + 15
d. 𝑠(𝑥) = 2𝑥 2 + 5𝑥 − 8 and 𝑝(𝑥) = 4𝑥 3 − 19𝑥 − 15
2. A company produces two sizes of a dog house, large and small. If 𝐿 represents the number of large dog
houses and 𝑆 represents the number of small dog houses, then the polynomial 230𝐿 + 160𝑆 + 100
describes the revenue from the sale of the dog houses. The polynomial 170𝐿 + 130𝑆 + 555 describes
the cost of producing the dog houses. Write an expression in simplest form for net profit from the sale
of the dog houses.
a. −60𝐿 − 30𝑆 + 455
c. 60𝐿 + 30𝑆 − 455
b. 400𝐿 + 290𝑆 + 655
d. 40𝐿 + 32𝑆 − 450
3. A company produces three sizes of a dog house, small, medium, and large. The small dog house sells for
$80, the medium size for $110, and the large for $140. The small dog houses cost $50 each to make,
medium $70 each, and large $79 each. Let 𝑠 represent the number of small size dog houses, 𝑚 represent
the number of medium size dog houses and 𝐿 represent the number of large size dog houses. Write an
expression in simplest form for the net profit.
a. 30𝑠 + 40𝑚 + 61𝐿
c. −28𝑠 − 43𝑚 − 76𝐿
b. −30𝑠 − 40𝑚 − 61𝐿
d. 28𝑠 + 43𝑚 + 76𝐿
4. Which of the following expressions are monomials with degree 2?
𝑖. 2𝑥 2 + 2𝑥
𝑖𝑖. 2𝑥 2
𝑖𝑖𝑖. 𝑥 2
𝑖𝑣. 2𝑥
a. 𝑖𝑖 and 𝑖𝑖𝑖
b. 𝑖𝑖 and 𝑖𝑣
c. 𝑖𝑖𝑖 and 𝑖𝑣
d. 𝑖 and 𝑖𝑖
5. Factor: 𝑥 2 − 12𝑥 + 36
a. (2𝑥 − 12)(2𝑥 + 12)
b. (2𝑥 − 12)(2𝑥 − 12)
c. (𝑥 − 6)(𝑥 + 6)
d. (𝑥 − 6)(𝑥 − 6)
6. Solve for the quotient and the remainder when you divide 𝑓(𝑥) = 𝑥 3 + 2𝑥 2 − 3𝑥 − 6 by 𝑥 + 2.
a. 𝑥 2 + 6𝑥 + 7, 𝑟 = 0
c. 𝑥 2 − 7, 𝑟 = 5
b. 𝑥 2 + 7, 𝑟 = 5
d. 𝑥 2 − 3, 𝑟 = 0
7. What are the zeros of 𝑓(𝑥) = 𝑥 3 − 12𝑥 2 + 21𝑥 + 98.
a. 2 and 7
b. 2 and −7
c. −2 and 7
d. −2 and −7
8. When you divide 𝑝(𝑥) = 2𝑥 3 − 3𝑥 2 + 5𝑥 − 1 by 𝑥 − 2, what is the remainder?
a. −1
b. 0
c. 13
d. 36
9. Which expression is the factored form of 𝑥 3 − 8 ?
a. (𝑥 + 2)(𝑥 2 + 2𝑥 + 4)
c. (𝑥 − 2)(𝑥 2 + 2𝑥 + 4)
b. (𝑥 + 2)3
d. (𝑥 − 2)(𝑥 2 + 4𝑥 + 4)
10. Which expression is the factored form of 𝑥 3 + 64 ?
a. (𝑥 − 4)(𝑥 2 + 4𝑥 + 16)
c. (𝑥 − 4)(𝑥 2 + 4𝑥 − 16)
2
b. (𝑥 + 4)(𝑥 + 4𝑥 + 16)
d. (𝑥 + 4)(𝑥 2 − 4𝑥 + 16)
DIRECTIONS: Match the polynomials in COLUMN A with its corresponding factors in COLUMN B.
COLUMN A
_____11. 𝑥 2 + 13𝑥 − 30
_____12. 9𝑥 2 − 30𝑥 + 25
_____13. 2𝑥 2 + 5𝑥 + 3
_____14. 3𝑥 2 − 16𝑥 + 5
_____15. 4𝑥 2 + 12𝑥 + 9
_____16. 𝑥 2 − 5𝑥 − 24
_____17. 𝑥 2 − 8𝑥 − 20
_____18. 3𝑥 2 + 7𝑥 + 2
_____19. 25𝑥 2 − 40𝑥 + 16
_____20. (9𝑥 2 − 78𝑥 + 25)
COLUMN B
𝑎. (3𝑥 − 1)(𝑥 − 5)
b. (2𝑥 + 3)(𝑥 + 1)
c. (3𝑥 + 1)(𝑥 + 2)
d. (2𝑥 + 3)(2𝑥 + 3)
e. (5𝑥 − 4)(5𝑥 − 4)
f. (3𝑥 − 5)(3𝑥 − 5)
g. (𝑥 − 10)(𝑥 + 2)
h. (𝑥 − 8)(𝑥 + 3)
i. (𝑥 + 15)(𝑥 − 2)
j. (3𝑥 − 1)(3𝑥 − 25)
SHOW YOUR SOLUTION TO GET FULL CREDIT.
21-23. Find the quotient and the remainder when you divide 𝑥 3 + 2𝑥 2 + 4𝑥 + 10 by (𝑥 − 2).
24-25. Factor the polynomial 9𝑥 2 + 18𝑥 − 7.