AnswersFL-1200330-Algebra 2 Sem 1 - FlexGraphing Polynomial Functions

Graphing Polynomial Functions — Unit test Answers

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What expression is equivalent to ?

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

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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
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What is the difference of the polynomials?

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What is the missing coefficient? =

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4
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8
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10
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22
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The volume of a cylinder is given by the formula , where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can?

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What is the fifth term in the binomial expansion of (x + 5)8?

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175,000x3
B
43,750x4
C
3,125x5
D
7,000x5
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Which expression is equivalent to ?

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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?

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What is the cube root of ?

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

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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?

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, , , 5
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, 1, , 11
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, , , , , 5, 11
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D
0, , , , , , 5, 11
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12

The area of a rectangle, A = l • w is represented by the expression . Which could be the dimensions of the rectangle?

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If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

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A
(x + 2)(x + 60)
B
(x – 2)(x – 60)
C
(x – 10)(x + 2)(x + 6)
D
(x + 10)(x – 2)(x – 6)
14

The polynomial function is graphed below.Which is a potential rational root of f(x) at point P?

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The root at point P may be .
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The root at point P may be .
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The root at point P may be .
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The root at point P may be .
Option D
15

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.

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4 inches
B
5 inches
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9 inches
D
10 inches
16

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
17

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

A
x – 2
B
x + 2
C
x – 4
D
x + 1
18

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
19

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

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A
–3, –2, 3
B
–3, 2
C
18, 32
D
18, 32, 66
20

The side length, s, of a cube is x – 2y. If V = s3, what is the volume of the cube?

A
x3 – 6x2y + 12xy2 – 8y3
B
x3 + 6x2y + 12xy2 + 8y3
C
3x3 – 6x2y + 12xy2 – 24y3
D
3x3 + 6x2y + 12xy2 + 24y3

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