AnswersAdvanced Algebra Concepts and ConnectionsModeling with Polynomial Functions: Polynomial Functions

Modeling with Polynomial Functions: Polynomial Functions — Test Answers

25 verified answers
1
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What are the roots of the polynomial equation?

A
negative 3 , 2
B
18 , 32 , 66
C
negative 3 , negative 2 , 3
D
18 , 32
2
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Which is a potential rational root of f of x at point cap p ?

A
The root at point cap p may be 1 third .
B
The root at point cap p may be 1 fifth .
C
The root at point cap p may be 5 thirds .
D
The root at point cap p may be 3 fifths .
3

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
3 x minus 5
C
2 x minus 1
D
2 x plus 1
4

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
5

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at open paren 0 comma 7 close paren Which statement must be true?

A
The slope of the line is not equal to 7 .
B
The circle has a radius equal to 7 .
C
The slope of the line is equal to 7 .
D
The circle has a radius greater than 7 .
6

What are the roots of the polynomial equation x cubed minus 7 x is equal to 6 x minus 12 ? Use a graphing calculator and a system of equations.

A
1 , 3
B
negative 4 , 1 , 3
C
negative 6 , 6
D
negative 3 , negative 1 , 4
7

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 x plus 2
B
f of x is equal to x squared minus 2 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
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 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).
B
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).
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 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).
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 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).
9

What is the completely factored form of x squared minus 16 x y plus 64 y squared ?

A
open paren x plus 8 y close paren times open paren x plus 8 y close paren
B
x y open paren x minus 16 plus 64 y close paren
C
x y open paren x plus 16 plus 64 y close paren
D
open paren x minus 8 y close paren times open paren x minus 8 y close paren
10

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at open paren 10 comma 6 close paren and passes through the point open paren 12 comma 7 close paren A commuter jet has filed a flight plan that takes it along a linear path from open paren negative 18 comma 14 close paren to open paren 16 comma negative 13 close paren Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

A
y is equal to 1 fourth times open paren x minus 10 close paren squared plus 6 y is equal to negative 2 x minus 22
B
y is equal to 1 fourth times open paren x minus 5 close paren squared plus 10 y is equal to negative 1 half x plus 5
C
y is equal to 1 fourth times open paren x minus 5 close paren squared plus 10 y is equal to negative 2 x minus 22
D
y is equal to 1 fourth times open paren x minus 10 close paren squared plus 6 y is equal to negative 27 over 34 x minus 5 over 17
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 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 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 plus 7 close paren open paren x plus 5 close paren open paren x minus 2 close paren
12

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 negative 7
B
x is equal to 1 and x is equal to 7
C
x is equal to negative 1 and x is equal to 5
D
x is equal to negative 5 and x is equal to 1
13

Which statement best describes the equation open paren x plus 5 close paren squared plus 4 times open paren x plus 5 close paren plus 12 is equal to 0 ?

A
The equation is not quadratic in form because there is no real solution.
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 quadratic in form because it can be rewritten as a quadratic equation with u substitution u is equal to open paren x plus 5 close paren .
14

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 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 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
D
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
15

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
2 with multiplicity 3 comma negative 4 with multiplicity 2 , and 1 with multiplicity 4
B
negative 2 with multiplicity 3 comma 4 with multiplicity 2 comma and negative 1 with multiplicity 4
C
2 with multiplicity 2 comma negative 4 with multiplicity 1 , and 1 with multiplicity 3
D
negative 2 with multiplicity 2 comma 4 with multiplicity 1 , and negative 1 with multiplicity 3
16

What is one of the solutions to the following system? y minus 3 is equal to x x squared minus 6 x plus 13 is equal to y

A
open paren negative 5 comma 2 close paren
B
open paren 8 comma 5 close paren
C
open paren negative 2 comma 1 close paren
D
open paren 2 comma 5 close paren
17

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 correct because the solutions are irrational.
C
She is correct because all solutions are intersection points of the graphs.
D
She is incorrect because systems may have only complex solutions which are not visible on a graph.
18

What is the completely factored form of p to the 4th power minus 16 ?

A
open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p plus 2 close paren
B
open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 2 p plus 4 close paren
C
open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren times open paren p minus 2 close paren
D
open paren p minus 2 close paren times open paren p plus 2 close paren times open paren p squared plus 4 close paren
19

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
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
B
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 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
D
plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5
20

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42 comma 000 ft squared What is a dimension of the parking lot?

A
210 ft
B
120 ft
C
205 ft
D
375 ft

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