AnswersAA - F26 Advanced AlgebraQuadratic in Form Polynomials

Quadratic in Form Polynomials — Unit test Answers

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21
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What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation?

A
u = (x + 5)
B
u = (x – 5)
C
u = (x + 5)2
D
u = (x – 5)2
22
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What is the quotient of the following division problem?

Question illustration
A
x + 2
B
x + 1
C
x2 + 3x + 2
D
0
23

Which quadratic equation is equivalent to (x2 – 1)2 – 11(x2 – 1) + 24 = 0?

A
u2 – 11u + 24 = 0 where u = (x2 – 1)
B
(u2)2 – 11(u2) + 24 where u = (x2 – 1)
C
u2 + 1 – 11u + 24 = 0 where u = (x2 – 1)
D
(u2 – 1)2 – 11(u2 – 1) + 24 where u = (x2 – 1)
24

What substitution should be used to rewrite 16(x3 + 1)2 – 22(x3 + 1) – 3 = 0 as a quadratic equation?

A
u = (x3)
B
u = (x3 + 1)
C
u = (x3 + 1)2
D
u = (x3 + 1)3
25

What is the quotient of (x3 – 3x2 + 5x – 3) ÷ (x – 1)?

A
x2 – 2x – 3
B
x2 + 2x + 7
C
x2 – 3x + 8
D
x2 – 2x + 3
26

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)
27

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
28

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
29

Which table describes the behavior of the graph of f(x) = 2x3 – 26x – 24?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
30

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
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
31

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
32

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
33

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
34

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
35

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.
36

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
37

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
38

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.
39

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

A
x – 2
B
x + 2
C
x – 4
D
x + 1
40

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

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