AnswersNY-Algebra II Term 1 HillcrestUnit Test

Unit Test — Unit test Answers

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The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

Question illustration
A
The root at point P may be .
Option A
B
The root at point P may be .
Option B
C
The root at point P may be .
Option C
D
The root at point P may be .
Option D
2
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Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

A
The graph of the function is positive on (–6, –2).
B
The graph of the function is negative on (, 0).
Option B
C
The graph of the function is positive on (–2, 4).
D
The graph of the function is negative on (4, ).
Option D
4

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

Question illustration
A
–4x8
B
–4x5
C
4x5
D
4x8
5

Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–3 + 2i, –3 – 2i
B
–2, –4
C
–2, –4, –3 + 2i, –3 – 2i
D
–2, –4, –3 + 2i, 3 + 2i
6

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

A
, , , 5
Option A
B
, 1, , 11
Option B
C
, , , , , 5, 11
Option C
D
0, , , , , , 5, 11
Option D
7

What is the remainder when (x4 + 36) is divided by (x2 – 8)?

A
36
B
64
C
100
D
117
8

The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows:• There have been two turning points in sales this year.• Sales are expected to increase in the long run.• The least amount of sales during the year is about $250,000.Which graph correctly shows the coffee shop’s sales?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient?

A
x cubed minus x squared + x minus 1
Option A
B
x3
C
x cubed + x squared + x + 1
Option C
D
x3 – 2
10

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

Question illustration
A
–3, –2, 3
B
–3, 2
C
18, 32
D
18, 32, 66
11

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Question illustration
A
(x + 2)(x + 60)
B
(x – 2)(x – 60)
C
(x – 10)(x + 2)(x + 6)
D
(x + 10)(x – 2)(x – 6)
12

The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly’s reasoning is correct or incorrect?

A
She is incorrect because systems may have only complex solutions which are not visible on a graph.
B
She is incorrect because the solutions may have multiplicity greater than 1.
C
She is correct because all solutions are intersection points of the graphs.
D
She is correct because the solutions are irrational.
13

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

A
x – 2
B
x + 2
C
x – 4
D
x + 1
14

Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 + i. Which statement describes the number and nature of all roots for this function?

A
f(x) has two real roots and one imaginary root.
B
f(x) has three real roots.
C
f(x) has five real roots.
D
f(x) has three real roots and two imaginary roots.
15

A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.

Question illustration
A
4 inches
B
5 inches
C
9 inches
D
10 inches
16

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
17

The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

A
x + 1 minus StartFraction 4 Over x Superscript 4 Baseline + 4 x cubed + 3 x squared + 8 x + 4 EndFraction
Option A
B
x + 1 + StartFraction 4 Over x Superscript 4 Baseline + 4 x cubed + 3 x squared + 8 x + 4 EndFraction
Option B
C
x + 1 minus StartFraction 4 Over x cubed + 3 x squared + 8 EndFraction
Option C
D
x + 1 + StartFraction 4 Over x cubed + 3 x squared + 8 EndFraction
Option D
18

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
19

Randy divides (2x4 – 3x3 – 3x2 + 7x – 3) by (x2 – 2x + 1) as shown below. What error does Randy make?

Question illustration
A
He makes a subtraction error.
B
He makes an error writing the constant term in the quotient.
C
He makes an error choosing the x-term in the quotient.
D
He makes an error rewriting the problem in long division.
20

Which statement describes the graph of this polynomial function?

Question illustration
A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 3.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –3.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –3.

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