AnswersAA - F26 Advanced AlgebraQuadratic in Form Polynomials

Quadratic in Form Polynomials — Cumulative exam Answers

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21
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What is the value of i 20+1?

A
1
B
–1
C
–i
D
i
22
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Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D
23

Given that (3, 2, –6) and (–2, 5, 1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?

A
The system can only be consistent and independent.
B
The system can be either inconsistent and independent or consistent and dependent.
C
The system can be either inconsistent and dependent or consistent and independent.
D
The system can only be inconsistent and dependent.
24

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.
25

Solve the system of equations.a.c.b.d.

Question illustration
A
A
B
B
C
C
D
D
26

What is the sum of 12 – 5i and –3 + 4i?

A
–16 + 63i
B
9 – i
C
9 – 9i
D
15 – 9i
27

The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

A
(–∞, –7)
B
(–∞, –1)
C
(–∞, 1)
D
(–∞, 7)
28

Solve the system of equations.a.c.b.d.

Question illustration
A
A
B
B
C
C
D
D
29

A company plans to sell embroidered hats for $15 each. The company’s financial planner estimates that the cost, y, of manufacturing the hats is a quadratic function with a y-intercept of 7,920 and a vertex of (150, 9,000). What is the minimum number of hats the company must sell to make a profit?

A
151
B
401
C
529
D
601
30

If f(x) = x2 – 25 and g(x) = x – 5, what is the domain of ?

Question illustration
A
all real values of x
B
all real values of x except x = 5
C
all real values of x except x = –5
D
all real values of x except x = 5 and x = –5
31

Dimitri is solving the equation x2 – 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

A
0
B
4
C
25
D
100
32

What are the domain and range of the function below?

Question illustration
A
domain: range:
Option A
B
domain: range:
Option B
C
domain: range:
Option C
D
domain: range:
Option D
33

An isosceles triangle has two sides of equal length. The third side is 7 less than twice the length of one of the other sides. If the perimeter of the triangle is 44 cm, what is the length of the third side?

A
9.25 cm
B
9.7 cm
C
12.75 cm
D
18.5 cm
34

What is one solution of the following system?

Question illustration
A
(–6, 0)
B
(–2, 4)
C
(0, –6)
D
(4, –2)
35

Which product of prime polynomials is equivalent to 4x5 – 6x4 + 4x3 – 6x2?

A
2x2(x2 + 1)(2x – 3)
B
2x2(x2 – 1)(2x + 3)
C
x2(x2 + 1)(2x – 3)
D
2(x2 – 1)(2x + 3)
36

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
37

What is the factorization of g3 – 125?

A
(g– 5)(g2 + 5g + 10)
B
(g – 25)(g2 + 25g + 625)
C
(g – 5)(g2 + 5g + 25)
D
(g – 25)(g2 + 5g + 125)
38

Samuel wants to buy at least twice as many graphic novels as comic books. Comic books sell for $7 each, and graphic novels sell for $12 each. Samuel can spend a maximum of $50. Let c represent the number of comic books, and let g represent the number of graphic novels. Which system of inequalities can be used to find the number of comic books and graphic novels Samuel can buy?

A
mc006-1.jpg
Option A
B
mc006-2.jpg
Option B
C
mc006-3.jpg
Option C
D
mc006-4.jpg
Option D
39

Which equation is an example of the commutative property of multiplication?

A
(4 + 2i) = (2i + 4)
B
(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)
C
(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)
D
(4 + 2i) = (4 + 2i + 0)
40

Which statement best describes the equation x5 + x3 – 14 = 0?

A
The equation is quadratic in form because it is a fifth-degree polynomial.
B
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2.
C
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
D
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.

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