AnswersAlgebra II - MA3111 A-CRUnit Test

Unit Test — Unit test Answers

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1
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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.
2
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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)
3

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
4

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.
5

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
6

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
7

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)
8

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
9

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
10

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
11

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
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

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 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
15

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).
16

A student factors 10x2 + 3x – 27 to the following. (2x – 3)(5x + 9) Which statement about (2x – 3)(5x + 9) is true?

A
The expression is equivalent, and it is completely factored.
B
The expression is equivalent, but it is not completely factored.
C
The expression is not equivalent, but it is completely factored.
D
The expression is not equivalent, and it is not completely factored.
17

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
18

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)
19

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
mc015-1.jpg
Option A
B
mc015-2.jpg
Option B
C
mc015-3.jpg
Option C
D
mc015-4.jpg
Option D
20

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.

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