AnswersAdvanced Algebra Concepts and Connections_TC_Online LearningUnit Test

Unit Test — Unit test Answers

25 verified answers
1
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What is the completely factored form of p4 – 16?

A
(p – 2)(p – 2)(p + 2)(p + 2)
B
(p – 2)(p – 2)(p – 2)(p – 2)
C
(p minus 2) (p + 2) (p squared + 2 p + 4)
Option C
D
(p minus 2) (p + 2) (p squared + 4)
Option D
2
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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
3

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

Question illustration
A
–6, 6
B
–4, 1, 3
C
–3, –1, 4
D
1, 3
4

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.
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

Which statement about –2h2 – 15h – 7 is true?

A
One of the factors is (h + 2).
B
One of the factors is (3h – 2).
C
One of the factors is (2h + 1).
D
One of the factors is (h – 7).
7

Which polynomial function has a leading coefficient of 2, root –4 with multiplicity 3, and root 10 with multiplicity 1?

A
f(x) = 2(x – 4)(x – 4)(x – 4)(x + 10)
B
f(x) = 2(x + 4)(x + 4)(x + 4)(x – 10)
C
f(x) = 3(x – 4)(x – 4)(x + 10)
D
f(x) = 3(x + 4)(x + 4)(x – 10)
8

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

A
Option
B
Option
C
✓ Correct
D
Option
9

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

A
(–6, 0.8)
B
(–6, 3.2)
C
(6, 3.2) ✓ Correct
D
(6, 0.8)
10

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
11

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
12

Which of the following describes the roots of the polynomial function ?

Question illustration
A
–2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3
B
–2 with multiplicity 3, 4 with multiplicity 2, and –1 with multiplicity 4
C
2 with multiplicity 2, –4 with multiplicity 1, and 1 with multiplicity 3
D
2 with multiplicity 3, –4 with multiplicity 2, and 1 with multiplicity 4
13

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
14

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
15

Which system is equivalent to ?

Question illustration
A
Option
B
Option
C
Option
D
✓ Correct
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

What is one of the solutions to the following system?

Question illustration
A
(–5, 2)
B
(–2, 1)
C
(2, 5) ✓ Correct
D
(8, 5)
18

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
19

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
20

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

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