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Polynomial Functions — Test Answers

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Which expression is a possible leading term for the polynomial function graphed?

A
4 x to the 8th power
B
negative 4 x to the 8th power
C
negative 4 x to the 5th power
D
4 x to the 5th power
2
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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 On a coordinate plane, the months are shown on the x axis from 0 to 10 and sales are shown in dollars from 0 to 900. A graph is drawn which has maxima at 500 and 800, minima at 300 and 250.
B
Image with description On a coordinate plane, the months are shown on the x axis from 0 to 10 and sales are shown in dollars from 0 to 900. The graph shows maxima at 425 and 900, minimum at 250.
C
Image with description On a coordinate plane, the months are shown on the x axis from 0 to 10 and sales are shown in dollars from 0 to 900. The graph shows maxima at 425 and 700, minimum at 200 and 150.
D
Image with description On a coordinate plane, the months are shown on the x axis from 0 to 10 and sales are shown in dollars from 0 to 900. The graph shows maxima at 450 and 525, minima at 250 and 0.
3

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 minus x squared plus x minus 1
B
x cubed
C
x cubed plus x squared plus x plus 1
D
x cubed minus 2
4

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 5 x cubed minus 7 x plus 11 ?

A
plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5
B
0 , plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
C
plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
D
plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
5

If open paren x minus 2 k close paren is a factor of f of x , which of the following must be true?

A
f of 2 k is equal to 0
B
A y -intercept of f of x is x is equal to 2 k .
C
A root of f of x is x is equal to negative 2 k .
D
f of open paren negative 2 k close paren is equal to 0
6

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 3 open paren x minus 4 close paren open paren x minus 4 close paren open paren x plus 10 close paren
B
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
C
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
D
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
7

A polynomial function has a root of negative 6 with multiplicity 1 , a root of negative 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 negative on open paren 4 comma infinity close paren .
B
The graph of the function is positive on open paren negative 6 comma negative 2 close paren .
C
The graph of the function is negative on open paren negative infinity comma 0 close paren .
D
The graph of the function is positive on open paren negative 2 comma 4 close paren .
8

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
Both ends of the graph will approach positive infinity.
B
The ends of the graph will approach zero.
C
The ends of the graph will extend in opposite directions.
D
Both ends of the graph will approach negative infinity.
9

Which statement describes the graph of this polynomial function? f of x is equal to x to the 5th power minus 6 x to the 4th power plus 9 x cubed

A
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to 3 .
B
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to 3 .
C
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to negative 3 .
D
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to negative 3 .
10

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 cubed minus 3 x squared plus 4 x minus 2
B
f of x is equal to x cubed minus x squared plus 4 x minus 2
C
f of x is equal to x squared minus x plus 2
D
f of x is equal to x squared minus 2 x plus 2
11

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 plus 7 close paren open paren x plus 5 close paren open paren x minus 2 close paren
C
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
D
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
12

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
15 million hoops
B
30 million hoops
C
1 point 4 million hoops
D
1 point 3 million hoops
13

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots square root of 5 and 2 ?

A
f of x is equal to 3 x squared minus 21 x plus 30
B
f of x is equal to x cubed minus 2 x squared minus 5 x plus 10
C
f of x is equal to 3 x cubed minus 6 x squared minus 15 x plus 30
D
f of x is equal to x squared minus 7 x plus 10
14

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 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).
B
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from (negative 3 point 8 comma 8), touches the x axis at (negative 3 comma 0), goes up to (negative 1 point 5 comma 3 point 5) and comes down to the origin. From here it goes down slightly and curves up to (2 point 1), curves down to touch x axis at (2 comma 0) and moves to quadrant 1 through the point (4 comma 8).
C
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 3, 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. From here it moves up slightly and passes through (2 comma 0), goes down, curves up at (2 comma negative 2), crosses x axis once again at (3 comma 0) and moves to quadrant 4 through the point (3 point 5 comma negative 8).
D
Image with description On a coordinate plane with x and y axes marked from negative 8 to 8, a polynomial graph is drawn. It starts from quadrant 1 passing through(negative 3 point 8 comma 8) crosses x axis at (negative 3 comma 0), goes down and curves up at (negative 2 comma negative 3 point 5), crosses the y axis at (0 comma negative 0 point 8). From here it touches the x axis at (1 comma 0), goes down slightly and again crosses the x axis at (3 comma 0), and moves to quadrant 1 through the point (4 comma 7).
15

What is the completely factored form of f of x is equal to 6 x cubed minus 13 x squared minus 4 x plus 15 ?

A
open paren x plus 1 close paren times open paren 2 x minus 3 close paren times open paren 3 x minus 5 close paren
B
open paren x plus 1 close paren times open paren 3 x minus 2 close paren times open paren 5 x minus 3 close paren
C
open paren x plus 1 close paren squared times open paren 2 x minus 3 close paren
D
open paren x plus 1 close paren times open paren 6 x squared minus 19 x plus 15 close paren
16

Three roots of a fifth degree polynomial function f of x are negative 2 , 2 , and 4 plus i Which statement describes the number and nature of all roots for this function?

A
f of x has two real roots and one imaginary root.
B
f of x has three real roots and two imaginary roots.
C
f of x has three real roots.
D
f of x has five real roots.
17

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 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'
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 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'
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, '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'
18

Which of the following describes the roots of the polynomial function f of x is equal to open paren x plus 2 close paren squared times open paren x minus 4 close paren times open paren x plus 1 close paren cubed ?

A
negative 2 with multiplicity 3 comma 4 with multiplicity 2 comma and negative 1 with multiplicity 4
B
2 with multiplicity 2 comma negative 4 with multiplicity 1 , and 1 with multiplicity 3
C
2 with multiplicity 3 comma negative 4 with multiplicity 2 , and 1 with multiplicity 4
D
negative 2 with multiplicity 2 comma 4 with multiplicity 1 , and negative 1 with multiplicity 3
19

Which of the following is the complete list of roots for the polynomial function f of x is equal to open paren x squared plus 6 x plus 8 close paren times open paren x squared plus 6 x plus 13 close paren ?

A
negative 2 , negative 4 , negative 3 plus 2 i , 3 plus 2 i
B
negative 2 , negative 4
C
negative 3 plus 2 i , negative 3 minus 2 i
D
negative 2 , negative 4 , negative 3 plus 2 i , negative 3 minus 2 i
20

According to the Rational Root Theorem, which is a factor of the polynomial f of x is equal to 3 x cubed minus 5 x squared minus 12 x plus 20 ?

A
3 x plus 5
B
2 x plus 1
C
2 x minus 1
D
3 x minus 5

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