AnswersAlgebra 2 with ProbabilityPolynomial Functions and Theorems

Polynomial Functions and Theorems — Test Answers

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1
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What are the possible degrees for the polynomial function?

A
even degrees of 6 or greater
B
degrees of 5 or greater
C
odd degrees of 5 or greater
D
degrees of 6 or greater
2
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Let A , b , and c be real numbers where A is not equal to b is not equal to c is not equal to 0 Which of the following functions could represent the graph?

A
f of x is equal to open paren x minus A close paren squared times open paren x minus b close paren times open paren x minus c close paren to the 6th power
B
f of x is equal to x squared open paren x minus A close paren squared open paren x minus b close paren to the 4th power open paren x minus c close paren
C
f of x is equal to x to the 4th power open paren x minus A close paren open paren x minus b close paren cubed open paren x minus c close paren cubed
D
f of x is equal to x cubed open paren x minus A close paren cubed open paren x minus b close paren open paren x minus c close paren squared
3

The formula for the volume of a cube is cap v times s is equal to s cubed where s is the side length of the cube. What is the domain and range of this function?

A
s is greater than 0 , cap v times s is less than 0
B
s is less than 0 , cap v times s is less than 0
C
s is less than 0 , cap v times s is greater than 0
D
s is greater than 0 , cap v times s is greater than 0
4

The price that a company charged for a basketball hoop is given by the equation 50 minus 5 x squared where x is the number of hoops that are produced, in millions. It costs the company 30 dollars 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?

A
1 point 4 million hoops
B
1 point 3 million hoops
C
15 million hoops
D
30 million hoops
5

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 the solutions may have multiplicity greater than 1.
B
She is incorrect because systems may have only complex solutions which are not visible on a graph.
C
She is correct because the solutions are irrational.
D
She is correct because all solutions are intersection points of the graphs.
6

Which statement describes how the graph of the given polynomial would change if the term negative 3 x to the 6th power is added? y is equal to 2 x to the 6th power plus 9 x to the 5th power minus 7 x cubed minus 1

A
The ends of the graph will approach zero.
B
Both ends of the graph will approach positive infinity.
C
The ends of the graph will extend in opposite directions.
D
Both ends of the graph will approach negative infinity.
7

Which table describes the behavior of the graph of f of x is equal to 2 x cubed minus 26 x minus 24 ?

A
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Above' Row 3: Column 1, '(−4, 1)'; Column 2, 'Below' Row 4: Column 1, '(1, 3)'; Column 2, 'Above' Row 5: Column 1, '(3, ∞)'; Column 2, 'Below'
B
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Above' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Below' Row 4: Column 1, '(−1, 4)'; Column 2, 'Above' Row 5: Column 1, '(4, ∞)'; Column 2, 'Below'
C
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 3 close paren'; Column 2, 'Below' Row 3: Column 1, 'open paren negative 3 comma negative 1 close paren'; Column 2, 'Above' Row 4: Column 1, '(−1, 4)'; Column 2, 'Below' Row 5: Column 1, '(4, ∞)'; Column 2, 'Above'
D
Table with 2 columns and 5 rows.Row 1: Column 1, 'Interval'; Column 2, 'Relation of graph to x-axis' Row 2: Column 1, 'open paren negative infinity comma negative 4 close paren'; Column 2, 'Below' Row 3: Column 1, '(−4, 1)'; Column 2, 'Above' Row 4: Column 1, '(1, 3)'; Column 2, 'Below' Row 5: Column 1, '(3, ∞)'; Column 2, 'Above'
8

A polynomial function has a root of negative 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
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from quadrant III, passing through the point negative 3 point 5 comma negative 8, touches the x axis at 3 comma 0, moves down and curves up at negative 1 point 8 comma 7, and passes through the origin. Here the curve moves up slightly and passes through the point 2 comma 0, goes down, curves up to the point 2 comma negative 2, crosses x axis once again at point 3 comma 0 and moves to quadrant IV through the point 3 point 5 comma negative 8.
B
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. The curve starts from negative 3 point 8 comma 8, touches the x axis at negative 3 comma 0, passes through the point negative 1 point 5 comma 3 point 5 and comes down to the origin. Here the curve goes down slightly and curves up to the point 2 point 1, curves down to touch x axis at point 2 comma 0 and moves to quadrant I through the point 4 comma 8.
C
Image with description On a coordinate plane, the x and y axes ranges from negative 8 to 8 with an increment of 1. The polynomial graph is drawn on the coordinate plane. It starts from quadrant I passing through the point negative 3 point 8 comma 8 crosses x axis at negative 3 comma 0, goes down and curves up at the point negative 2 comma negative 3 point 5, crosses the y axis at the point 0 comma negative 0 point 8. Here the curve touches the x axis at point 1 comma 0, goes down slightly and again crosses the x axis at point 3 comma 0, and moves to quadrant I through the point 4 comma 7.
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. The graph starts from quadrant 3 passing through the point (negative 3 point 5 comma negative 8), it crosses the x axis at (negative 3 comma 0) moves up and curves down at (negative 2 comma 7), crosses the y axis at (0 comma 1), crosses the x axis at (1 comma 0), moves up and curves down at (2 point 5 comma 1). It then moves down, crosses x axis at (2 comma 0) and moves to quadrant 4 through the point (4 comma negative 8).
9

What is the polynomial function of lowest degree with leading coefficient 1 and roots 1 and 1 plus i ?

A
f of x is equal to x squared minus 2 x plus 2
B
f of x is equal to x squared minus x plus 2
C
f of x is equal to x cubed minus x squared plus 4 x minus 2
D
f of x is equal to x cubed minus 3 x squared plus 4 x minus 2
10

The owner of a coffee shop chain creates a graph representing sales in thousands of dollars. She describes the characteristics as follows: • There have been two turning points in sales this year. • Sales are expected to increase in the long run. • The least amount of sales during the year is about 250 dollars comma 000 Which graph correctly shows the coffee shop’s sales?

A
Image with description Line graph on an x y coordinate plane. The x-axis is labeled from 1 to 9. The y-axis is labeled from 100 to 900 in increments of 100. The curve begins at approximately (0 comma 200), rises to a local maximum at (1 point 5 comma 425), then decreases to a local minimum near (5 point 5 comma 150), and subsequently increases sharply to approximately (10 comma 700).
B
Image with description Line graph on an x y coordinate plane. The x-axis is labeled from 1 to 9. The y-axis is labeled from 100 to 900 in increments of 100. The curve begins near (0 comma 450), decreases to a local minimum at approximately (1 point 5 comma 250), then increases to a local maximum at approximately (5 point 5 comma 525), and finally decreases sharply, passing through (9 comma 50) and continuing downwards.
C
Image with description Line graph on an x y coordinate plane. The x-axis is labeled from 1 to 9. The y-axis is labeled from 100 to 900 in increments of 100. The curve begins near (0 comma 425), decreases to a local minimum at approximately (3 point 5 comma 250), then rises sharply, ending with an arrow near (10, 900) indicating an upward path.
D
Image with description Line graph on an x y coordinate plane. The x-axis is labeled from 1 to 9. The y-axis is labeled from 100 to 900 in increments of 100. The curve begins at approximately (0 comma 300), rises to a local maximum at (1 point 5 comma 525), then decreases to a local minimum near (5 comma 250), and subsequently increases sharply to approximately (10 comma 800).
11

Which best describes the end behavior of y is equal to negative 2 x cubed ?

A
As x is greater than 0 increases, f of x decreases. As x is less than 0 decreases, f of x decreases.
B
As x is greater than 0 increases, f of x increases. As x is less than 0 decreases, f of x increases.
C
As x is greater than 0 increases, f of x decreases. As x is less than 0 decreases, f of x increases.
D
As x is greater than 0 increases, f of x increases. As x is less than 0 decreases, f of x decreases.
12

Which polynomial function has a leading coefficient of 1 , roots negative 2 and 7 with multiplicity 1 , and root 5 with multiplicity 2 ?

A
f of x is equal to open paren x plus 7 close paren times open paren x plus 5 close paren times open paren x plus 5 close paren times open paren x minus 2 close paren
B
f of x is equal to 2 open paren x minus 7 close paren open paren x minus 5 close paren open paren x plus 2 close paren
C
f of x is equal to 2 open paren x plus 7 close paren open paren x plus 5 close paren open paren x minus 2 close paren
D
f of x is equal to open paren x minus 7 close paren times open paren x minus 5 close paren times open paren x minus 5 close paren times open paren x plus 2 close paren
13

Use synthetic division to solve open paren x to the 4th power minus 1 close paren divided by open paren x minus 1 close paren What is the quotient?

A
x cubed
B
x cubed plus x squared plus x plus 1
C
x cubed minus x squared plus x minus 1
D
x cubed minus 2
14

The real root of the equation x cubed plus 10 x squared plus 29 x plus 30 is equal to 0 is negative 6 What are the nonreal solutions?

A
negative 4 plus 2 i comma negative 4 minus 2 i
B
2 plus i comma 2 minus i
C
negative 2 plus i comma negative 2 minus i
D
4 plus 2 i comma 4 minus 2 i
15

Which polynomial function has a leading coefficient of 2 , root negative 4 with multiplicity 3 , and root 10 with multiplicity 1 ?

A
f of x is equal to 2 open paren x plus 4 close paren open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
B
f of x is equal to 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
C
f of x is equal to 2 open paren x minus 4 close paren open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
D
f of x is equal to 3 open paren x plus 4 close paren open paren x plus 4 close paren open paren x minus 10 close paren
16

Which equation is quadratic in form?

A
3 x to the 5th power plus 8 x cubed plus 6 is equal to 0
B
5 x to the 6th power plus x to the 4th power plus 12 is equal to 0
C
x to the 9th power plus x cubed minus 10 is equal to 0
D
6 x to the 4th power plus 7 x squared minus 3 is equal to 0
17

What are the solutions of the equation open paren x minus 3 close paren squared plus 2 times open paren x minus 3 close paren minus 8 is equal to 0 ? Use u substitution to solve.

A
x is equal to negative 1 and x is equal to 5
B
x is equal to negative 5 and x is equal to 1
C
x is equal to negative 1 and x is equal to negative 7
D
x is equal to 1 and x is equal to 7
18

If f of negative 2 is equal to 0 , what are all the factors of the function f of x is equal to x cubed minus 2 x squared minus 68 x minus 120 ? Use the Remainder Theorem.

A
open paren x plus 2 close paren times open paren x plus 60 close paren
B
open paren x minus 2 close paren times open paren x minus 60 close paren
C
open paren x minus 10 close paren times open paren x plus 2 close paren times open paren x plus 6 close paren
D
open paren x plus 10 close paren times open paren x minus 2 close paren times open paren x minus 6 close paren
19

Which statement describes the function y is equal to A x to the n th power when A is equal to 1 and n is odd?

A
The graph does not pass through the origin.
B
The graph is symmetric about the origin.
C
The graph has more than one x -intercept.
D
The graph opens down.
20

The real roots for the equation x to the 4th power minus x cubed plus 10 x squared minus 16 x minus 96 is equal to 0 are negative 2 and 3 What are the nonreal solutions?

A
negative 2 i comma 2 i
B
negative 16 i comma 16 i
C
negative 4 i comma 4 i
D
negative i comma i

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