AnswersCommon Core Algebra II A-ICGeometric Series

Geometric Series — Unit test Answers

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1
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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
2
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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.
3

What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i?

A
f(x) = x2 – 2x + 2
B
f(x) = x3 – x2 + 4x – 2
C
f(x) = x3 – 3x2 + 4x – 2
D
f(x) = x2 – x + 2
4

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

A
mc012-1.jpg
Option A
B
mc012-2.jpg
Option B
C
mc012-3.jpg
Option C
D
mc012-4.jpg
Option D
5

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
6

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

Question illustration
A
1.3 million hoops
B
1.4 million hoops
C
15 million hoops
D
30 million hoops
7

A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?

A
$1,451.00
B
$2,095.89
C
$2,149.63
D
$2,167.54
8

Which equation is quadratic in form?

A
3x5 + 8x3 + 6 = 0
B
6x4 + 7x2 – 3 = 0
C
5x6 + x4 + 12 = 0
D
x9 + x3 – 10 = 0
9

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
10

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
11

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.
12

If (x – 2k) is a factor of f(x), which of the following must be true?

A
f(2k) = 0
B
f(–2k) = 0
C
A root of f(x) is x = –2k.
D
A y intercept of f(x) is x = 2k.
13

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots and 2?

Question illustration
A
f (x) = 3 x cubed minus 6 x squared minus 15 x + 30
Option A
B
f (x) = x cubed minus 2 x squared minus 5 x + 10
Option B
C
f (x) = 3 x squared minus 21 x + 30
Option C
D
f (x) = x squared minus 7 x + 10
Option D
14

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

A
112.50 ft2
B
145.31 ft2
C
147.66 ft2
D
290.63 ft2
15

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

A
x = –5 and x = 1
B
x = –1 and x = 5
C
x = –1 and x = –7
D
x = 1 and x = 7
16

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.
17

According to the Rational Root Theorem, which is a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

A
2x + 1
B
2x – 1
C
3x + 5
D
3x – 5
18

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
19

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

A
(x + 1)(6x2 – 19x + 15)
B
(x + 1)2(2x – 3)
C
(x + 1)(3x – 2)(5x – 3)
D
(x + 1)(2x – 3)(3x – 5)
20

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)

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