AnswersLA-Algebra II AUnit Test

Unit Test — Unit test Answers

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1
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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
2
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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
3

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.
4

Which expression is a sum of cubes?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
5

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
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

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
8

What is the cube root of ?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
9

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.
10

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)
11

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)
12

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

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