AnswersTX-Algebra II A-CRMixed Degree Systems

Mixed Degree Systems — Unit test Answers

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One root of a third degree polynomial function f(x) is –5 + 2i. 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 two imaginary roots and one real root.
C
f(x) has three imaginary roots.
D
f(x) has three real roots.
2
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Which of the following is the complete list of roots for the polynomial function ?

Question illustration
A
–5, 3
B
–5, 3, –4 + i, –4 – i
C
–5, 3, –4 + i, 4 + i
D
–4 + i, –4 – i
3

Which statement about 4x2 + 19x – 5 is true?

A
One of the factors is (x – 4).
B
One of the factors is (4x + 1).
C
One of the factors is (4x – 5).
D
One of the factors is (x + 5).
4

If f(–5) = 0, what are all the factors of the function ? Use the Remainder Theorem.

Question illustration
A
(x – 2)(x + 5)(x – 3)
B
(x + 2)(x – 5)(x + 3)
C
(x – 2)(x + 5)
D
(x + 2)(x – 5)
5

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.

A
x = ±2 and x = ±3
B
x = ±2i and x = ±3
C
x = ±2 and x = ±3i
D
x = ±2i and x = ±3i
6

Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

A
$0.40
B
$2.50
C
$3.75
D
$4.00
7

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

A
f(x) = 3x2 + 5x + 4
B
f(x) = 3x2 + 15x + 12
C
f(x) = 3x2 – 5x + 4
D
f(x) = 3x2 – 15x + 12
8

What is the completely factored form of ?

Question illustration
A
(2x - 5)(3x + 1)
B
(2x + 5)(3x - 1)
C
(2x - 1)(3x - 5)
D
(2x + 1)(3x + 5)
9

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

A
f(k) = 0
B
f(–k) = 0
C
A root of f(x) is x = k.
D
A y intercept of f(x) is x = –k.
10

Which polynomial function has x-intercepts –1, 0, and 2 and passes through the point (1, –6)?

A
f(x) = x3 – x2 – 2x
B
f(x) = 3x3 – 3x2 – 6x
C
f(x) = x3 + x2 – 2x
D
f(x) = 3x3 + 3x2 – 6x
11

Which second degree polynomial function has a leading coefficient of 2 and roots –3 and 5?

A
f(x) = 2x2 + 4x – 30
B
f(x) = 2x2 + 2x – 15
C
f(x) = 2x2 – 4x – 30
D
f(x) = 2x2 – 2x – 15
12

Which statement about the polynomial function g(x) is true?

A
If all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
B
If all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
C
If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
D
If the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.
13

Which statement describes the graph of this polynomial function?

Question illustration
A
The graph crosses the x-axis at x = 2 and x = –1 and touches the x-axis at x = 0.
B
The graph touches the x-axis at x = 2 and x = –1 and crosses the x-axis at x = 0.
C
The graph crosses the x-axis at x = –2 and x = 1 and touches the x-axis at x = 0.
D
The graph touches the x-axis at x = –2 and x = 1 and crosses the x-axis at x = 0.
14

Which is a factor of f(x) = 60x4 + 86x3 – 46x2 – 43x + 8? Use the Rational Root Theorem to help you find your answer.

A
x – 6
B
5x – 8
C
6x – 1
D
8x + 5
15

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Sharon jumps, Megan throws a beach ball up to Sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?

A
0.65 seconds
B
0.92 seconds
C
1.08 seconds
D
1.15 seconds

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