AnswersCR - Algebra 2 26-27 - S1Quadratic in Form Polynomials

Quadratic in Form Polynomials — Unit test Answers

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1
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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
2
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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
3

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)
4

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
5

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

A
36
B
64
C
100
D
117
6

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

A
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).
B
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
C
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
D
The equation is not quadratic in form because there is no real solution.
7

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

A
x – 2
B
x + 2
C
x – 4
D
x + 1
8

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)
9

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.
10

What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

A
x = StartFraction negative 4 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option A
B
x = StartFraction negative 7 plus-or-minus StartRoot 5 EndRoot Over 2 EndFraction
Option B
C
x = –7 and x = –2
D
x = –1 and x = 4
11

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
12

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
13

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.
14

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
15

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
16

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
17

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
18

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
19

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
20

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

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