Question 1

Find the zeros of the polynomial function.
-$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x$

Accepted Answer

A)  $x = 0 , x = - 5$ 
B)  $x = 0 , x = 5$ 
C)  $x = 1 , x = - 5$ 
D)  $x = 0 , x = 5 , x = - 5$ 
A)  $x = 0 , x = - 5$ 
B)  $x = 0 , x = 5$ 
C)  $x = 1 , x = - 5$ 
D)  $x = 0 , x = 5 , x = - 5$

Question 2

Determine the constant of variation for the stated condition.
-If $y$ varies directly as the cube of $x$, and $y = 5$ when $x = 2$, find $y$ when $x = 8$.

Accepted Answer

A)  320 
B)  20 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 5 } { 64 }$ 
A)  320 
B)  20 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 5 } { 64 }$

Question 3

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-Crosses the $x$-axis at $- 1,0$, and 4 ; lies below the $x$-axis between $- 1$ and 0 ; lies above the $x$-axis between 0 and $4 .$

Accepted Answer

A)  $f ( x ) = - x ^ { 3 } + 3 x ^ { 2 } + 4 x$ 
B)  $f ( x ) = - x ^ { 3 } - 3 x ^ { 2 } + 4 x$ 
C)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x$ 
D)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x$ 
A)  $f ( x ) = - x ^ { 3 } + 3 x ^ { 2 } + 4 x$ 
B)  $f ( x ) = - x ^ { 3 } - 3 x ^ { 2 } + 4 x$ 
C)  $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 4 x$ 
D)  $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 4 x$

Question 4

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = 5 ( x + 3 ) ( x - 5 ) ^ { 3 }$$

Accepted Answer

A)  $- 3$, multiplicity 1 , crosses $x$-axis; 5 , multiplicity 3 , crosses $x$-axis 
B)  3, multiplicity 1 , crosses $x$-axis; $- 5$, multiplicity 3 , crosses $x$-axis 
C)  -3, multiplicity 1 , crosses $x$-axis; 5 , multiplicity 3 , touches $x$-axis and turns around 
D)  3 , multiplicity 1 , touches $x$-axis; $- 5$, multiplicity 3 , touches $x$-axis and turns around 
A)  $- 3$, multiplicity 1 , crosses $x$-axis; 5 , multiplicity 3 , crosses $x$-axis 
B)  3, multiplicity 1 , crosses $x$-axis; $- 5$, multiplicity 3 , crosses $x$-axis 
C)  -3, multiplicity 1 , crosses $x$-axis; 5 , multiplicity 3 , touches $x$-axis and turns around 
D)  3 , multiplicity 1 , touches $x$-axis; $- 5$, multiplicity 3 , touches $x$-axis and turns around

Question 5

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = ( x - 2 ) ( x - 1 ) ( 5 x - 7 )$$

Accepted Answer

A)  2 
B)  5 
C)  3 
D)  0 
A)  2 
B)  5 
C)  3 
D)  0

Question 6

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { ( x - 8 ) ( 2 x + 5 ) } { x ^ { 2 } + 2 x - 4 }$

Accepted Answer

A)  $( 8,0 )$ and $\left( - \frac { 5 } { 2 } , 0 \right)$ 
B)  $( - 8,0 )$ and $\left( \frac { 5 } { 2 } , 0 \right)$ 
C)  $( 8,0 )$ and $( - 5,0 )$ 
D)  none 
A)  $( 8,0 )$ and $\left( - \frac { 5 } { 2 } , 0 \right)$ 
B)  $( - 8,0 )$ and $\left( \frac { 5 } { 2 } , 0 \right)$ 
C)  $( 8,0 )$ and $( - 5,0 )$ 
D)  none

Question 7

The graph of a quadratic function is given. Determine the function's equation.
-

Accepted Answer

A)  $h ( x ) = x ^ { 2 } - 2$ 
B)  $g ( x ) = x ^ { 2 } + 4 x + 4$ 
C)  $f ( x ) = x ^ { 2 } - 4 x + 4$ 
D)  $j ( x ) = x ^ { 2 } + 2$ 
A)  $h ( x ) = x ^ { 2 } - 2$ 
B)  $g ( x ) = x ^ { 2 } + 4 x + 4$ 
C)  $f ( x ) = x ^ { 2 } - 4 x + 4$ 
D)  $j ( x ) = x ^ { 2 } + 2$

Question 8

Divide using long division.
-$$\left( 5 x ^ { 4 } - 38 x ^ { 3 } + 22 x ^ { 2 } - 11 x + 28 \right) \div ( 7 - x )$$

Accepted Answer

A)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x + 4$ 
B)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4$ 
C)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4 + \frac { 56 } { 7 }$ 
D)  $- 5 x ^ { 3 } + 3 x ^ { 2 } + x - 4$ 
A)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x + 4$ 
B)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4$ 
C)  $- 5 x ^ { 3 } + 3 x ^ { 2 } - x - 4 + \frac { 56 } { 7 }$ 
D)  $- 5 x ^ { 3 } + 3 x ^ { 2 } + x - 4$

Question 9

Use the graph or table to determine a solution of the equation. Use synthetic division to verify that this number is a
solution of the equation. Then solve the polynomial equation.
-$x^{3}+6 x^{2}+11 x+6=0$

Accepted Answer

A)  $- 1$; The remainder is zero; $- 1 , - 2$, and $- 3$, or $\{ - 3 , - 2 , - 1 \}$ 
B)  $- 1$; The remainder is zero; $1 , - 2$, and $- 3$, or $\{ - 3 , - 2,1 \}$ 
C)  $- 1$; The remainder is zero; $- 1,2$, and $- 3$, or $\{ - 3 , - 1,2 \}$ 
D)  $- 1$; The remainder is zero; $- 1 , - 2$, and 3 , or $\{ - 2 , - 1,3 \}$ 
A)  $- 1$; The remainder is zero; $- 1 , - 2$, and $- 3$, or $\{ - 3 , - 2 , - 1 \}$ 
B)  $- 1$; The remainder is zero; $1 , - 2$, and $- 3$, or $\{ - 3 , - 2,1 \}$ 
C)  $- 1$; The remainder is zero; $- 1,2$, and $- 3$, or $\{ - 3 , - 1,2 \}$ 
D)  $- 1$; The remainder is zero; $- 1 , - 2$, and 3 , or $\{ - 2 , - 1,3 \}$

Question 10

Solve the problem.
-The revenue achieved by selling x graphing calculators is figured to be x(42 - 0.5x) dollars. The cost of each calculator is $22. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $182.00?

Accepted Answer

A)  between 14 and 26 calculators 
B)  between 19 and 31 calculators 
C)  between 15 and 25 calculators 
D)  between 16 and 24 calculators 
A)  between 14 and 26 calculators 
B)  between 19 and 31 calculators 
C)  between 15 and 25 calculators 
D)  between 16 and 24 calculators

Question 11

Determine the constant of variation for the stated condition.
-$\mathrm { y }$ varies directly as $\mathrm { z }$ and $\mathrm { y } = 180$ when $\mathrm { z } = 12$. Find $\mathrm { y }$ when $\mathrm { z } = 13$.

Accepted Answer

A)  195 
B)  169 
C)  225 
D)  144 
A)  195 
B)  169 
C)  225 
D)  144

Question 12

Write an equation that expresses the relationship. Use k as the constant of variation.
-a varies inversely as the square of $y$.

Accepted Answer

A)  $a = \frac { k } { v ^ { 2 } }$ 
B)  $a = \frac { y ^ { 2 } } { k }$ 
C)  $a = \frac { k } { \sqrt { y } }$ 
D)  $a = \frac { \sqrt { y } } { k }$ If y varies inversely as x, find the inverse variation equation for the situation. 
A)  $a = \frac { k } { v ^ { 2 } }$ 
B)  $a = \frac { y ^ { 2 } } { k }$ 
C)  $a = \frac { k } { \sqrt { y } }$ 
D)  $a = \frac { \sqrt { y } } { k }$ If y varies inversely as x, find the inverse variation equation for the situation.

Question 13

Divide using synthetic division.
-$$\frac { x ^ { 5 } + x ^ { 2 } - 3 } { x - 2 }$$

Accepted Answer

A)  $x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 9 x + 18 + \frac { 33 } { x - 2 }$ 
B)  $x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } + 10 x + 20 + \frac { 37 } { x - 2 }$ 
C)  $x ^ { 4 } + 3 x ^ { 2 } + \frac { 3 } { x - 2 }$ 
D)  $x ^ { 4 } + 3 + \frac { 3 } { x - 2 }$ 
A)  $x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 9 x + 18 + \frac { 33 } { x - 2 }$ 
B)  $x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } + 10 x + 20 + \frac { 37 } { x - 2 }$ 
C)  $x ^ { 4 } + 3 x ^ { 2 } + \frac { 3 } { x - 2 }$ 
D)  $x ^ { 4 } + 3 + \frac { 3 } { x - 2 }$

Question 14

Determine whether the function is a polynomial function.
-$$f ( x ) = \frac { 9 - x ^ { 3 } } { 5 }$$

Accepted Answer

A)  3 
B)  $- \frac { 1 } { 5 }$ 
C)  0 
D)  9 
A)  3 
B)  $- \frac { 1 } { 5 }$ 
C)  0 
D)  9

Question 15

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { x } { x + 3 } > 0$$

Accepted Answer

A)  $( - \infty , - 3 )$ or $( 0 , \infty )$
  
B)  $( - 3,0 ]$
  
C)  $( - \infty , - 3 ]$ or $[ 0 , \infty )$
  
D)  $( 0 , \infty )$
  
A)  $( - \infty , - 3 )$ or $( 0 , \infty )$
  
B)  $( - 3,0 ]$
  
C)  $( - \infty , - 3 ]$ or $[ 0 , \infty )$
  
D)  $( 0 , \infty )$

Question 16

Write an equation that expresses the relationship. Use k as the constant of variation.
-If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 15 kilograms accelerates at a rate of 2 meters per second per second by a force, find the rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force.

Accepted Answer

A)  10 meters per second per second 
B)  $\frac { 2 } { 5 }$ meters per second per second 
C)  8 meters per second per second 
D)  5 meters per second per second 
A)  10 meters per second per second 
B)  $\frac { 2 } { 5 }$ meters per second per second 
C)  8 meters per second per second 
D)  5 meters per second per second

Question 17

Use transformations of f(x) $$f ( x ) = \frac { 1 } { x } \text { or } f ( x ) = \frac { 1 } { x ^ { 2 } }$$ to graph the rational function.
-$$f ( x ) = \frac { 1 } { ( x + 4 ) ^ { 2 } } + 3$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } - 9$$

Accepted Answer

A)  $( 0,0 )$ and $( - 6,0 )$ 
B)  $( 0,0 )$ and $( 6,0 )$ 
C)  $( 0,0 )$ and $( - 9,0 )$ 
D)  $( 6,0 )$ and $( - 6,0 )$ 
A)  $( 0,0 )$ and $( - 6,0 )$ 
B)  $( 0,0 )$ and $( 6,0 )$ 
C)  $( 0,0 )$ and $( - 9,0 )$ 
D)  $( 6,0 )$ and $( - 6,0 )$

Question 19

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = 6 + 5 x + x ^ { 2 }$$

Accepted Answer

A)  $( - 3,0 )$ and $( - 2,0 )$ 
B)  $( 3,0 )$ and $( 2,0 )$ 
C)  $( 3,0 )$ and $( - 2,0 )$ 
D)  $( - 3,0 )$ and $( 2,0 )$ 
A)  $( - 3,0 )$ and $( - 2,0 )$ 
B)  $( 3,0 )$ and $( 2,0 )$ 
C)  $( 3,0 )$ and $( - 2,0 )$ 
D)  $( - 3,0 )$ and $( 2,0 )$

Question 20

Determine whether the function is a polynomial function.
-$$f ( x ) = \pi x ^ { 3 } + 7 x ^ { 2 } + 4$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Find the zeros of the polynomial function. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x$

Determine the constant of variation for the stated condition. -If $y$ varies directly as the cube of $x$ , and $y = 5$ when $x = 2$ , find $y$ when $x = 8$ .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = 5 ( x + 3 ) ( x - 5 ) ^ { 3 }$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = ( x - 2 ) ( x - 1 ) ( 5 x - 7 )$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { ( x - 8 ) ( 2 x + 5 ) } { x ^ { 2 } + 2 x - 4 }$

The graph of a quadratic function is given. Determine the function's equation. -

Divide using long division. - $\left( 5 x ^ { 4 } - 38 x ^ { 3 } + 22 x ^ { 2 } - 11 x + 28 \right) \div ( 7 - x )$

Solve the problem. -The revenue achieved by selling x graphing calculators is figured to be x(42 - 0.5x) dollars. The cost of each calculator is $22. How many graphing calculators must be sold to make a profit (revenue - cost) of at least $182.00?

Determine the constant of variation for the stated condition. - $\mathrm { y }$ varies directly as $\mathrm { z }$ and $\mathrm { y } = 180$ when $\mathrm { z } = 12$ . Find $\mathrm { y }$ when $\mathrm { z } = 13$ .

Write an equation that expresses the relationship. Use k as the constant of variation. -a varies inversely as the square of $y$ .

Divide using synthetic division. - $\frac { x ^ { 5 } + x ^ { 2 } - 3 } { x - 2 }$

Determine whether the function is a polynomial function. - $f ( x ) = \frac { 9 - x ^ { 3 } } { 5 }$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = ( x + 3 ) ^ { 2 } - 9$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = 6 + 5 x + x ^ { 2 }$

Determine whether the function is a polynomial function. - $f ( x ) = \pi x ^ { 3 } + 7 x ^ { 2 } + 4$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 3: Polynomial and Rational Functions

Find the zeros of the polynomial function. - f(x)=x3+10x2+25xf ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 xf(x)=x3+10x2+25x

Determine the constant of variation for the stated condition. -If yyy varies directly as the cube of xxx , and y=5y = 5y=5 when x=2x = 2x=2 , find yyy when x=8x = 8x=8 .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=5(x+3)(x−5)3f ( x ) = 5 ( x + 3 ) ( x - 5 ) ^ { 3 }f(x)=5(x+3)(x−5)3

Determine the maximum possible number of turning points for the graph of the function. - f(x)=(x−2)(x−1)(5x−7)f ( x ) = ( x - 2 ) ( x - 1 ) ( 5 x - 7 )f(x)=(x−2)(x−1)(5x−7)

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=(x−8)(2x+5)x2+2x−4f ( x ) = \frac { ( x - 8 ) ( 2 x + 5 ) } { x ^ { 2 } + 2 x - 4 }f(x)=x2+2x−4(x−8)(2x+5)​