Name: ________________________ Class: ___________________ Date: __________
ID: A
Chapter 8A: Factoring Polynomials Unit Review
PART I Multiple Choice: Answer all questions in this part. Each correct answer will receive 2 credits.
No partial credit will be allowed.
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2
1. Which expression is equivalent to 9x − 16?
a. (3x + 4)(3x − 4)
b. (3x − 4)(3x − 4)
c. (3x + 8)(3x − 8)
d. (3x − 8)(3x − 8)
2
2. Factored completely, the expression 2y + 12y − 54 is equivalent to
a. 2(y + 9)(y − 3)
b. 2(y − 3)(y − 9)
c. (y + 6)(2y − 9)
d. (2y + 6)(y − 9)
2
2
3. Factored, the expression 16x − 25y is equivalent to
a. (4x − 5y)(4x + 5y)
b. (4x − 5y)(4x − 5y)
c. (8x − 5y)(8x + 5y)
d. (8x − 5y)(8x − 5y)
2
4. Which expression is a factor of x + 2x − 15?
a. (x + 3)
b. (x + 15)
c. (x − 5)
d. (x − 3)
2
5. What are the factors of x − 2x − 24?
a. (x − 4)(x + 6)
b. (x − 12)(x + 2)
c. (x + 12)(x − 2)
d. (x + 4)(x − 6)
3
2 2
2
6. If one factor of 21xy − 15x y is 3xy , what is the other factor?
2
a. 7x − 5y
2
2
b. 7y − 5x
c. 7y − 5x
2
d. 7xy − 5x
1
Name: ________________________
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ID: A
2
2
7. What is a common factor of x − 9 and x + x − 6?
a. x − 3
2
b. x
c. x + 3
d. x − 2
2
8. If 4x is one factor of 4x − 12x, what is the other factor?
2
a. x − 8x
b. x − 3
c. 4x
d. x + 3
a.
2
− 14d + 49
2
(d + 7)
9. Factor d
2
b. (d − 7)
c. (d − 7)(d + 7)
d. (d − 49)(d − 1)
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10. Which expression represents
3
2
12x − 6x + 2x
in simplest form?
2x
2
6x − 3x
2
b. 10x − 4x
2
c. 6x − 3x + 1
2
d. 10x − 4x + 1
a.
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2
2
11. When 3g − 4g + 2 is subtracted from 7g + 5g − 1, the difference is
2
a. −4g − 9g + 3
2
b. 4g + g + 1
2
c. 4g + 9g − 3
2
d. 10g + g + 1
12. What is the value of p in the equation 8p + 2 = 4p − 10?
a. 1
b. −1
c. 3
d. −3
2
Name: ________________________
ID: A
PART II: Answer all questions in this part. Clearly indicate the necessary steps, including appropriate
formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical
answer with no work shown will receive only 1 credit.
2
13. Factor completely: 8n − 50
Answer:___________________________
2
14. What are the factors of x − 10x + 24?
Answer:___________________________
3
Name: ________________________
ID: A
2
15. Factor completely: 5x − 40x + 60
Answer:___________________________
ÏÔ
Ô y < −3x + 2
. Give one ordered pair that is a
16. BONUS: Graph the system of linear inequalities ÔÌÔ
ÔÔ y ≥ 4x − 1
Ó
solution.
One Solution of System:________________________________
4
ID: A
Chapter 8A: Factoring Polynomials Unit Review
Answer Section
MULTIPLE CHOICE
1. ANS:
TOP:
2. ANS:
TOP:
3. ANS:
TOP:
4. ANS:
TOP:
5. ANS:
TOP:
6. ANS:
TOP:
7. ANS:
TOP:
8. ANS:
TOP:
9. ANS:
REF:
NAT:
KEY:
10. ANS:
TOP:
11. ANS:
TOP:
12. ANS:
TOP:
A
PTS: 2
REF: 080902ia
STA: A.A.19
Factoring the Difference of Perfect Squares
A
PTS: 2
REF: 060623a
STA: A.A.20
Factoring Polynomials
A
PTS: 2
REF: 060804ia
STA: A.A.19
Factoring the Difference of Perfect Squares
D
PTS: 2
REF: 010004a
STA: A.A.20
Factoring Polynomials
D
PTS: 2
REF: 010318a
STA: A.A.20
Factoring Polynomials
C
PTS: 2
REF: 060318a
STA: A.A.20
Factoring Polynomials
C
PTS: 2
REF: 010414a
STA: A.A.19
Factoring the Difference of Perfect Squares
B
PTS: 2
REF: 060421a
STA: A.A.20
Factoring Polynomials
B
PTS: 2
DIF: L2
9-7 Factoring Special Cases
OBJ: 9-7.1 Factoring Perfect-Square Trinomials
ADP J.1.4
STA: NY A.A.19 | NY A.A.20
TOP: 9-7 Example 1
polynomial | factoring trinomials | perfect-square trinomial
C
PTS: 2
REF: 011011ia
STA: A.A.14
Rational Expressions
C
PTS: 2
REF: 080819ia
STA: A.A.13
Addition and Subtraction of Polynomials
D
PTS: 2
REF: 010807a
STA: A.A.22
Solving Equations
SHORT ANSWER
13. ANS:
2(2n + 5)(2n − 5)
PTS: 2
REF: 080533a
STA: A.A.19
TOP: Factoring the Difference of Perfect Squares
14. ANS:
(x − 4)(x − 6)
PTS:
2
REF: 010318a
STA: A.A.20
1
TOP: Factoring Polynomials
ID: A
15. ANS:
5(x − 2)(x − 6)
PTS: 2
REF: 060535a
16. ANS:
(0, 0) and (−4, −5) are solutions.
(2, 2) and (10, 1) are not solutions.
STA: A.A.20
TOP: Factoring Polynomials
Graph y < −3x + 2 and y ≥ 4x − 1 on the same coordinate plane. The solutions of the system are the
overlapping shaded regions, including the solid boundary line.
PTS: 4
DIF: Average
REF: Page 422
OBJ: 6-6.2 Solving a System of Linear Inequalities by Graphing
NAT: 12.5.4.g
STA: A.G.7
TOP: 6-6 Solving Systems of Linear Inequalities
2