AnswersAZ-Common Core Algebra II ADivision of Polynomials

Division of Polynomials — Unit test Answers

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Which is equivalent to , and what type of special product is it?

Question illustration
A
; a perfect square trinomial
Option A
B
; the difference of squares
Option B
C
; a perfect square trinomial
Option C
D
; the difference of squares
Option D
2
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Mrs. Ishimitsu is installing a rubber bumper around the edge of her coffee table. The dimensions of the rectangular table are (2x2 – 16) feet and (–x2 + 4x + 1) feet. Which expression represents the total perimeter of the table, and if x = 3, what is the length of the entire rubber bumper?

A
x2 + 4x – 15; 3 feet
B
x2 + 4x – 15; 6 feet
C
2x2 + 8x – 30; 6 feet
D
2x2 + 8x – 30; 12 feet
3

If (x – 5) is a factor of f(x), which of the following must be true?

A
A root of f(x) is x = –5.
B
A root of f(x) is x = 5.
C
Both x = –5 and x = 5 are roots of f(x).
D
Neither x = –5 nor x = 5 is a root of f(x).
4

If (x + k) is a factor of f(x), which of the following must be true?

A
f(k) = 0
B
f(–k) = 0
C
A root of f(x) is x = k.
D
A y intercept of f(x) is x = –k.
5

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
6

Which polynomial is in standard form?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
7

The variables X, Y, and Z represent polynomials where X = a, Y = 3a – 5, and Z = a2 + 2. What is X2Y – Z in simplest form?

A
2a2 – 5a – 2
B
3a3 – 6a2 – 2
C
–3a3 – 2
D
–3a2 – 2
8

Anja divides (8x3 – 36x2 + 54x – 27) by (2x – 3) as shown below. What error does Anja make?

Question illustration
A
She makes a subtraction error.
B
She makes an error choosing the x-term in the quotient.
C
She makes a multiplication error.
D
She makes an error rewriting the problem in long division.
9

Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold.

A
27x – 650
B
27x + 390
C
33x – 650
D
33x + 390
10

Armando used algebra tiles to represent the product .

Question illustration
A
He used the algebra tiles correctly.
B
He did not represent the two original factors correctly.
C
The signs on some of the products are incorrect.
D
Some of the products do not show the correct powers of x.
11

What is the remainder when (3x3 – 2x2 + 4x – 3) is divided by (x2 + 3x + 3)?

A
30
B
3x – 11
C
28x – 36
D
28x + 30
12

What is the difference of the two polynomials?(7y2 + 6xy) – (–2xy + 3)

A
7y2 + 4xy – 3
B
7y2 + 8xy – 3
C
7y2 + 4xy + 3
D
7y2 + 8xy + 3
13

What is the product?

Question illustration
A
negative 81 t squared minus 16
Option A
B
negative 81 t squared + 16
Option B
C
negative 81 t squared minus 72 t + 16
Option C
D
negative 81 t squared + 72 t + 16
Option D
14

The polynomial 8x2 – 8x + 2 – 5 + x is simplified to 8x2 – gx – h. What are the value of g and h?

A
g = –9 and h = 7
B
g = 9 and h = –3
C
g = –7 and h = 7
D
g = 7 and h = 3
15

The price that a company charged for a computer accessory is given by the equation where x is the number of accessories that are produced, in millions. It costs the company $10 to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

Question illustration
A
1.45 million
B
3.45 million
C
40 million
D
48 million
16

What is the quotient?x + 5 )4x2 + 14x − 9

A
4x + 6 +
Option A
B
4x + 6 −
Option B
C
4x − 6 +
Option C
D
4x − 6 −
Option D
17

What is the product?

Question illustration
A
2 x squared minus 3
Option A
B
2 x squared + 6 x
Option B
C
2 x squared + 5 x minus 3
Option C
D
2 x squared + 6 x minus 3
Option D
18

The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). If area = length × width, what is the length of the rectangle?

A
x + 5
B
x – 15
C
x + 15
D
x – 5
19

What is the quotient of (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?

A
2 x Superscript 4 Baseline minus 3 x cubed minus eleven-halves
Option A
B
2x2 + x – 3 –
Option B
C
2x2 – x
D
2x2 + x – 3
20

Which expression is a possible leading term for the polynomial function graphed below?

Question illustration
A
–18x14
B
–10x7
C
17x12
D
22x9

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