AnswersSummer_Advanced AlgebraUnit Test

Unit Test — Unit test Answers

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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
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

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
4

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
5

What is the factored form of ?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
6

Which expression is a sum of cubes?

A
mc012-1.jpg
Option A
B
mc012-2.jpg
Option B
C
mc012-3.jpg
Option C
D
mc012-4.jpg
Option D
7

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.
8

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
9

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

A
f(x) = 2(x + 7)(x + 5)(x – 2)
B
f(x) = 2(x – 7)(x – 5)(x + 2)
C
f(x) = (x + 7)(x + 5)(x + 5)(x – 2)
D
f(x) = (x – 7)(x – 5)(x – 5)(x + 2)
10

A cube with side length is stacked on another cube with side length . What is the total volume of the cubes in factored form?

Question illustration
A
mc025-3.jpg
Option A
B
mc025-4.jpg
Option B
C
mc025-5.jpg
Option C
D
mc025-6.jpg
Option D
11

What is the cube root of ?

Question illustration
A
mc008-2.jpg
Option A
B
mc008-3.jpg
Option B
C
mc008-4.jpg
Option C
D
mc008-5.jpg
Option D

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