AnswersAA - F26 Advanced AlgebraQuadratic in Form Polynomials

Quadratic in Form Polynomials — Unit test Answers

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A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?

A
The graph of the function is positive on (–6, –2).
B
The graph of the function is negative on (, 0).
Option B
C
The graph of the function is positive on (–2, 4).
D
The graph of the function is negative on (4, ).
Option D
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What is the remainder when (x4 + 36) is divided by (x2 – 8)?

A
36
B
64
C
100
D
117
43

If (x – 2k) is a factor of f(x), which of the following must be true?

A
f(2k) = 0
B
f(–2k) = 0
C
A root of f(x) is x = –2k.
D
A y intercept of f(x) is x = 2k.
44

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

A
(x + 1)(6x2 – 19x + 15)
B
(x + 1)2(2x – 3)
C
(x + 1)(3x – 2)(5x – 3)
D
(x + 1)(2x – 3)(3x – 5)
45

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x2(x – a)2(x – b)4(x – c)
B
f(x) = x3(x – a)3(x – b)(x – c)2
C
f(x) = x4(x – a)(x – b)3(x – c)3
D
f(x) = (x – a)2(x – b)(x – c)6
46

According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9x4 – 2x2 – 3x + 4?

A
, , , , , 1, , 2, 4
Option A
B
, , , 1, , , 3, , 9
Option B
C
, , , , , 1, , 2, 4
Option C
D
, , , 1, , , 3, , 9
Option D
47

Which of the following graphs could be the graph of the function ?

Question illustration
A
mc018-2.jpg
Option A
B
mc018-3.jpg
Option B
C
mc018-4.jpg
Option C
D
mc018-5.jpg
Option D
48

The quotient of (x4 + 5x3 – 3x – 15) and (x3 – 3) is a polynomial. What is the quotient?

A
x7 + 5x6 – 6x4 – 30x3 + 9x + 45
B
x – 5
C
x + 5
D
x7 + 5x6 + 6x4 + 30x3 + 9x + 45
49

Which statement describes the graph of f(x) = 4x7 + 40x6 + 100x5?

A
The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5.
B
The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5.
C
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
D
The graph touches the x-axis at x = 0 and crosses the x-axis at x = –5.
50

What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

A
As , and as , .
Option A
B
As , and as , .
Option B
C
As , and as , .
Option C
D
As , and as , .
Option D
51

Shelia is dividing x4 – 4x3 + 4x2 – 6x + 5 by x – 1 using a division table. QuotientDivisor x3– 3x2+ x– 5xx4–3x3x2A– 1–x33x2BCWhat are the missing values in the table?

A
A = –5x; B = 1x; C = 5
B
A = –5x; B = –1x; C = 5
C
A = 5x; B = –1x; C = 5
D
A = 5x; B = 1x; C = 5
52

One root of is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Question illustration
A
(x + 6)(x + 8)
B
(x – 6)(x – 8)
C
(x – 2)(x + 4)(x – 6)
D
(x + 2)(x – 4)(x + 6)
53

Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?

A
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
Option A
B
x squared minus x + 1
Option B
C
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
Option C
D
x cubed minus x squared + x minus 1
Option D
54

At which root does the graph of f(x) = (x + 4)6(x + 7)5 cross the x-axis?

A
–7
B
–4
C
4
D
7
55

Use synthetic division to solve . What is the quotient?

Question illustration
A
4 x squared minus 27 x + 167 minus StartFraction 996 Over x minus 6 EndFraction
Option A
B
4 x squared + 21 x + 131 + StartFraction 792 Over x + 6 EndFraction
Option B
C
4 x squared + 21 x + 131 + StartFraction 792 Over x minus 6 EndFraction
Option C
D
4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction
Option D

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