AnswersAlgebra IIPolynomial Functions

Practice Test Answers

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What are the roots of the polynomial equation x to the 4th power plus x cubed is equal to 4 x squared plus 4 x ? Use a graphing calculator and a system of equations.

A
negative 2 , negative 1 , 0 , 2
B
negative 2 , 0 , 1 , 2
C
negative 1 , 0
D
0 , 1
2
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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
A root of f of x is x is equal to negative 5 .
C
Both x is equal to negative 5 and x is equal to 5 are roots of f of x .
D
A root of f of x is x is equal to 5 .
3

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

Which geometric series diverges?

A
the sum from n is equal to 1 to infinity of 2 thirds
B
the sum from n is equal to 1 to infinity of negative 12
C
3 fifths plus 3 tenths plus 3 over 20 plus 3 over 40 plus dot dot dot
D
negative 10 plus 4 minus 8 fifths plus 16 over 25 minus dot dot dot
5

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 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 .
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 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 .
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 negative 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 negative 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 infinity and as x rightarrow infinity , y rightarrow infinity .
7

If 5 plus 6 i is a root of the polynomial function f of x , which of the following must also be a root of f of x ?

A
6 plus 5 i
B
negative 5 minus 6 i
C
5 minus 6 i
D
6 minus 5 i
8

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
1
B
10 thirds
C
negative 5 halves
D
negative 2
9

What are the roots of the polynomial equation x cubed minus 6 x is equal to 3 x squared minus 8 ? Use a graphing calculator and a system of equations.

A
negative 5 , 4 , 40
B
negative 2 , 1 , 4
C
negative 40 , negative 4 , 5
D
negative 4 , negative 1 , 2
10

Which fraction represents the decimal 0 point 8 8 8 8 dot dot dot ?

A
80 over 99
B
the fraction with numerator 1 comma 111 and denominator 1 comma 250
C
9 eighths
D
8 ninths
11

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 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
B
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
C
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
D
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
12

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
3 point 4 5 million
B
40 million
C
48 million
D
1 point 4 5 million
13

Let A and b be real numbers where A is not equal to b is not equal to 0 Which of the following functions could represent the graph?

A
f of x is equal to x squared open paren x minus A close paren to the 5th power open paren x minus b close paren
B
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 squared
C
f of x is equal to x open paren x minus A close paren squared open paren x minus b close paren to the 4th power
D
f of x is equal to x open paren x minus A close paren cubed open paren x minus b close paren squared
14

Which polynomial function could be represented by the graph?

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

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