AnswersAdvanced Algebra Concepts and ConnectionsModeling with Polynomial Functions: Polynomial Functions

Practice Test Answers

20 verified answers2 views
1
Free Preview

What is the completely factored form of 6 x squared minus 13 x minus 5 ?

A
open paren 2 x minus 5 close paren times open paren 3 x plus 1 close paren
B
open paren 2 x plus 1 close paren times open paren 3 x plus 5 close paren
C
open paren 2 x plus 5 close paren times open paren 3 x minus 1 close paren
D
open paren 2 x minus 1 close paren times open paren 3 x minus 5 close paren
3

The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

A
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
B
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
C
plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
D
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
4

What is one solution of the following system? 2 y minus 2 x is equal to 12 x squared plus y squared is equal to 36

A
open paren negative 2 comma 4 close paren
B
open paren negative 6 comma 0 close paren
C
open paren 0 comma negative 6 close paren
D
open paren 4 comma negative 2 close paren
5

Which second degree polynomial function has a leading coefficient of 2 and roots negative 3 and 5 ?

A
f of x is equal to 2 x squared minus 4 x minus 30
B
f of x is equal to 2 x squared plus 4 x minus 30
C
f of x is equal to 2 x squared plus 2 x minus 15
D
f of x is equal to 2 x squared minus 2 x minus 15
6

What is the end behavior of the graph of the polynomial function f of x is equal to negative x to the 5th power plus 9 x to the 4th power minus 18 x cubed ?

A
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .
B
As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .
C
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .
D
As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow negative infinity .
7

Which statement describes the graph of this polynomial function? f of x is equal to x to the 4th power plus x cubed minus 2 x squared

A
The graph touches the x -axis at x is equal to 2 and x is equal to negative 1 and crosses the x -axis at x is equal to 0 .
B
The graph touches the x -axis at x is equal to negative 2 and x is equal to 1 and crosses the x -axis at x is equal to 0 .
C
The graph crosses the x -axis at x is equal to negative 2 and x is equal to 1 and touches the x -axis at x is equal to 0 .
D
The graph crosses the x -axis at x is equal to 2 and x is equal to negative 1 and touches the x -axis at x is equal to 0 .
8

A polynomial function has a root of negative 6 with multiplicity 3 and a root of 2 with multiplicity 4 If the function has a negative leading coefficient and is of odd 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 quadrant 3 passing through (negative 8 comma negative 1 point 5), it touches x axis at (negative 6 comma 0) and moves down and curves up at (negative 0 point 5 comma negative 3). It then passes through x axis at (2 comma 0) and moves to quadrant 1 passing through (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. It starts from quadrant 2, passes through (negative 8 comma 8), crosses the x axis at (negative 6 comma 0), moves down and curves up at (negative 3 point 5 comma negative 3), and crosses the y axis at (0 comma negative 1). It then touches the x axis at (2 comma 0) and moves to quadrant 4 passing through (6 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 2 passing through (negative 8 comma 0 point 9), touches the x axis at (negative 6 comma 0), it curves up and passes through y axis at (0 comma 1 point 5). It then crosses x axis at (2 comma 0) moves to quadrant 4 through (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 (5 comma 8), touches x axis at (2 comma 0), curves up and passes through y axis at (0 comma 2). It then moves up and curves down at (negative 3 point 5 comma 6), passes through x axis at (negative 6 comma 0) and moves to quadrant 3 passing through (negative 7 comma negative 8).
10

Which system is equivalent to the given system? y is equal to 9 x squared x plus y is equal to 5

A
y is equal to 3 x x plus 3 x is equal to 5
B
5 plus x is equal to 9 x squared y is equal to 5 plus x
C
y is equal to 9 y squared minus 90 y plus 225 x is equal to y minus 5
D
5 minus x is equal to 9 x squared y is equal to 5 minus x
12

A store owner puts in an order for product cap x and product cap y for a total of 4 comma 000 units. It costs 0 point 1 0 dollars per item to ship of product cap x and 0 point 0 4 dollars per item to ship product cap y If the total shipping cost is 352 dollars , which system of equations can be used to determine how much of product cap x and product cap y the store owner bought?

A
x plus y is equal to 4 comma 000 0 point 1 x plus 0 point 0 4 y is equal to 352
B
x plus y is equal to 4 comma 000 10 x plus 4 y is equal to 352
C
0 point 1 x plus 0 point 0 4 y is equal to 4 comma 000 x plus y is equal to 352
D
10 x plus 4 y is equal to 4 comma 000 x plus y is equal to 352
13

If open paren x minus 5 close paren is a factor of f of x , which of the following must be true?

A
Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .
B
Both x is equal to negative 5 and x is equal to 5 are roots of f of x .
C
A root of f of x is x is equal to 5 .
D
A root of f of x is x is equal to negative 5 .
15

What are the solutions of the equation x to the 4th power minus 5 x squared minus 36 is equal to 0 ? Use factoring to solve.

A
x is equal to plus or minus 2 i and x is equal to plus or minus 3
B
x is equal to plus or minus 2 and x is equal to plus or minus 3
C
x is equal to plus or minus 2 i and x is equal to plus or minus 3 i
D
x is equal to plus or minus 2 and x is equal to plus or minus 3 i
16

Which statement best describes the equation x to the 5th power plus x cubed minus 14 is equal to 0 ?

A
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
B
The equation is quadratic in form because it is a fifth-degree polynomial.
C
The equation is quadratic in form because the difference of the exponent of the lead term and the exponent of the middle term is 2 .
D
The equation is not quadratic in form because the exponent of the lead term is not the square of the exponent of the middle term.
17

What is the completely factored form of 12 x y minus 9 x minus 8 y plus 6 ?

A
3 x open paren 4 y minus 3 close paren minus 2 times open paren 4 y plus 3 close paren
B
negative 6 x open paren 4 y minus 3 close paren open paren 4 y minus 3 close paren
C
open paren 3 x minus 2 close paren times open paren 4 y minus 3 close paren times open paren 4 y minus 3 close paren
D
open paren 3 x minus 2 close paren times open paren 4 y minus 3 close paren
18

Which second degree polynomial function f of x has a leading coefficient of 3 and roots 4 and 1 ?

A
f of x is equal to 3 x squared minus 5 x plus 4
B
f of x is equal to 3 x squared plus 5 x plus 4
C
f of x is equal to 3 x squared plus 15 x plus 12
D
f of x is equal to 3 x squared minus 15 x plus 12

Did you find these answers helpful?