AnswersAlgebra IIPolynomials

Practice Test Answers

14 verified answers
1
Free Preview

A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?

A
6 or less
B
exactly 5
C
exactly 6
D
5 or less
2
Free Preview

According to the Rational Root Theorem, the following are potential roots of f of x is equal to 6 x to the 4th power plus 5 x cubed minus 33 x squared minus 12 x plus 20 negative 5 halves , negative 2 , 1 , 10 thirds Which is an actual root of f of x ?

A
10 thirds
B
1
C
negative 2
D
negative 5 halves
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
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
B
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 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
4

Which term, when added to the given polynomial, will change the end behavior of the graph? y is equal to 14 x to the 8th power minus 6 x to the 5th power minus 2 x to the 4th power minus 10

A
6 x to the 10th power
B
negative 6 x to the 9th power
C
negative 5 x to the 7th power
D
5 x to the 8th power
5

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 A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The enters from the upper-left quadrant near "negative 8 comma 1" with an arrowhead pointing upward and to the left. It drops slightly to a local minimum tangent to the x-axis at "negative 6 comma 0", then rises gradually through the second quadrant, crossing the y-axis at a local maximum near "0 comma 1 point 5". From there, it enters the first quadrant, crossing the x-axis at " 2 comma 0", and curves steeply downward into the fourth quadrant where it terminates with a downward-pointing arrowhead near "5 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 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 A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins in the third quadrant near "negative 8 comma negative 1 point 5" with a downward-pointing arrow. Moving right, it rises into the second quadrant to a local maximum tangent to the x-axis at "negative 6 comma 0". It then decreases gradually to a local minimum in the third quadrant near "negative 1 comma negative 3". From there, it curves upward, crossing the y-axis at "0 comma negative 2 point 8", passing through the x-axis at "2 comma 0, and rising steeply into the first quadrant, where it terminates with an upward-pointing arrow near "4 comma 8".
D
Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 8 to 8 with an increment of 1. The curve begins at point arrow near "negative 7 comma negative 8" and extends upward from the lower-left quadrant. It rises sharply, crossing the x-axis at "negative 6 comma 0", and reaches a local maximum near "negative 3 point 5 comma 6". From there, it moves downward through the second quadrant, crossing the y-axis at "0 comma 2", and enters the first quadrant. It reaches a local minimum tangent to the x-axis at "2 comma 0", and then curves steeply upwards, terminating with an upward-pointing arrow near "5 comma 8".
6

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 2 x minus 15
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 4 x minus 30
7

The price that a company charged for a computer accessory is given by the equation 100 minus 10 x squared where x is the number of accessories that are produced, in millions. It costs the company 10 dollars to make each accessory. The company currently produces 2 million accessories and makes a profit of 100 million dollars. What other number of accessories produced yields the same profit?

A
1 point 4 5 million
B
40 million
C
3 point 4 5 million
D
48 million
8

What is the cube root of negative 729 A to the 9th power b to the 6th power ?

A
negative 8 A squared b cubed
B
negative 8 A cubed b squared
C
negative 9 A squared b cubed
D
negative 9 A cubed b squared
9

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 i
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
D
x is equal to plus or minus 2 and x is equal to plus or minus 3 i
10

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

A
A root of f of x is x is equal to negative 5 .
B
A root of f of x is x is equal to 5 .
C
Neither x is equal to negative 5 nor x is equal to 5 is a root of f of x .
D
Both x is equal to negative 5 and x is equal to 5 are roots of f of x .
11

Which expression is a difference of cubes?

A
x to the 8th power minus 6
B
x to the 6th power minus 6
C
x to the 6th power minus 8
D
x to the 8th power minus 8
12

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 15 x plus 12
C
f of x is equal to 3 x squared plus 5 x plus 4
D
f of x is equal to 3 x squared minus 15 x plus 12
13

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 negative infinity and as x rightarrow infinity , y rightarrow negative infinity .
B
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow infinity .
C
As x rightarrow negative infinity , y rightarrow negative infinity and as x rightarrow infinity , y rightarrow infinity .
D
As x rightarrow negative infinity , y rightarrow infinity and as x rightarrow infinity , y rightarrow negative infinity .
14

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

A
The equation is quadratic in form because it is a fifth-degree polynomial.
B
The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
C
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.
D
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 .

Did you find these answers helpful?

More from this Course

practice test
14 verified answers

Practice Test

practice test
12 verified answers

Practice Test

practice test
7 verified answers

Practice Test