Given 3 + i is a root, determine all other roots of f(x) = x5 - 8x4 + 24x3 - 32x2 + 20x.

A) x = 1 - i, 3 - i B) x = 1 - i, 3 - i, 0 C) x = 1 + i, 3 - i D) x = 1 ± i, 3 - i, 0 E) x = 1 + i, 3 - i, 0 A) x = 1 - i, 3 - i B) x = 1 - i, 3 - i, 0 C) x = 1 + i, 3 - i D) x = 1 ± i, 3 - i, 0 E) x = 1 + i, 3 - i, 0

Find all the real zeros of f(x) = 4x3 - 12x2 - 15x - 4.

A) x = $\frac { 1 } { 4 }$ , 2 B) x = $- \frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ C) x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ D) x = $- \frac { 1 } { 2 }$ , 4 E) x = $- \frac { 1 } { 2 }$ , -4 A) x = $\frac { 1 } { 4 }$ , 2 B) x = $- \frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ C) x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ D) x = $- \frac { 1 } { 2 }$ , 4 E) x = $- \frac { 1 } { 2 }$ , -4

Exam 2: Polynomial and Rational Functions

A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility.The floor area of the current facility is rectangular and measures 290 feet by 80 feet.The manufacturer wants to increase each dimension by the same amount.

(Multiple Choice)

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Question 21

Given 3 + i is a root, determine all other roots of f(x) = x⁵ - 8x⁴ + 24x³ - 32x² + 20x.

(Multiple Choice)

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Question 22

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100$ . Select the correct graph of the cost function.

(Multiple Choice)

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Question 23

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ Inequality: $y \leq 2$

(Multiple Choice)

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Question 24

Select the correct rational function for the following graph.

(Multiple Choice)

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Question 25

Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

(Multiple Choice)

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Question 26

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

(Multiple Choice)

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Question 27

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } - x ^ { 2 } - 12 x + 7$

(Multiple Choice)

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Question 28

Find all the real zeros of f(x) = 4x³ - 12x² - 15x - 4.

(Multiple Choice)

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Question 29

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 1 } { x - 7 }$

(Multiple Choice)

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Question 30

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$ Inequality: $y \leq 0$

(Multiple Choice)

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Question 31

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical. $f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)$ , $g ( x ) = - 4 x ^ { 4 }$

(Multiple Choice)

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Question 32

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

(Multiple Choice)

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Question 33

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 3 x > 4$

(Multiple Choice)

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Question 34

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13$ .

(Multiple Choice)

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Question 35

Find all the zeros of the function. (t - 4)(t - 3)(t - 6i)(t + 6i)

(Multiple Choice)

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Question 36

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $\sqrt { - 39 }$

(Multiple Choice)

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Question 37

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

(Multiple Choice)

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Question 38

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by $R ( p ) = - 25 p ^ { 2 } + 1900 p$ Where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.

(Multiple Choice)

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Question 39

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

(Multiple Choice)

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Question 40

A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility.The floor area of the current facility is rectangular and measures 290 feet by 80 feet.The manufacturer wants to increase each dimension by the same amount.

Given 3 + i is a root, determine all other roots of f(x) = x⁵ - 8x⁴ + 24x³ - 32x² + 20x.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100$ . Select the correct graph of the cost function.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ Inequality: $y \leq 2$

Select the correct rational function for the following graph.

Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } - x ^ { 2 } - 12 x + 7$

Find all the real zeros of f(x) = 4x³ - 12x² - 15x - 4.

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 1 } { x - 7 }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$ Inequality: $y \leq 0$

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical. $f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)$ , $g ( x ) = - 4 x ^ { 4 }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 3 x > 4$

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13$ .

Find all the zeros of the function. (t - 4)(t - 3)(t - 6i)(t + 6i)

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $\sqrt { - 39 }$

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by $R ( p ) = - 25 p ^ { 2 } + 1900 p$ Where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Given 3 + i is a root, determine all other roots of f(x) = x5 - 8x4 + 24x3 - 32x2 + 20x.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by C=255p100−p,0≤p≤100C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100C=100−p255p​,0≤p≤100 . Select the correct graph of the cost function.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: y=5x2x2+25y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }y=x2+255x2​ Inequality: y≤2y \leq 2y≤2

Select the correct rational function for the following graph.

Find the zeros of the rational function. f(x)=1−5x−10f ( x ) = 1 - \frac { 5 } { x - 10 }f(x)=1−x−105​

Determine the domain of f(x)=6x+6x2−6xf ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }f(x)=x2−6x6x+6​ .

Select the correct graph of the following function. f(x)=5x3−x2−12x+7f ( x ) = 5 x ^ { 3 } - x ^ { 2 } - 12 x + 7f(x)=5x3−x2−12x+7

Find all the real zeros of f(x) = 4x3 - 12x2 - 15x - 4.

Find vertical and horizontal asymptotes. f(x)=1x−7f ( x ) = \frac { 1 } { x - 7 }f(x)=x−71​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: y=6(x−6)x+5y = \frac { 6 ( x - 6 ) } { x + 5 }y=x+56(x−6)​ Inequality: y≤0y \leq 0y≤0

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical. f(x)=−(4x4−3x3+16x)f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)f(x)=−(4x4−3x3+16x) , g(x)=−4x4g ( x ) = - 4 x ^ { 4 }g(x)=−4x4

Find the domain of the function and identify any vertical and horizontal asymptotes. f(x)=x+4x2−16f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }f(x)=x2−16x+4​

Solve the inequality and graph the solution on the real number line. x2+3x>4x ^ { 2 } + 3 x > 4x2+3x>4

Describe the right-hand and the left-hand behavior of the graph of q(x)=−5x4+12x3+13q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13q(x)=−5x4+12x3+13 .

Find all the zeros of the function. ​ (t - 4)(t - 3)(t - 6i)(t + 6i) ​

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. −39\sqrt { - 39 }−39​

If x=6x = \sqrt { 6 }x=6​ is a root of x3+5x2−6x−30=0x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0x3+5x2−6x−30=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p)=−25p2+1900pR ( p ) = - 25 p ^ { 2 } + 1900 pR(p)=−25p2+1900p Where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.

A farmer has 216 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Given 3 + i is a root, determine all other roots of f(x) = x⁵ - 8x⁴ + 24x³ - 32x² + 20x.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by $C = \frac { 255 p } { 100 - p } , 0 \leq p \leq 100$ . Select the correct graph of the cost function.

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ Inequality: $y \leq 2$

Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

Determine the domain of $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } - 6 x }$ .

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } - x ^ { 2 } - 12 x + 7$

Find all the real zeros of f(x) = 4x³ - 12x² - 15x - 4.

Find vertical and horizontal asymptotes. $f ( x ) = \frac { 1 } { x - 7 }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$ Inequality: $y \leq 0$

Select the correct graph of the functions f and g which shows the right-hand and left-hand behaviors of f and g appear identical. $f ( x ) = - \left( 4 x ^ { 4 } - 3 x ^ { 3 } + 16 x \right)$ , $g ( x ) = - 4 x ^ { 4 }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

Solve the inequality and graph the solution on the real number line. $x ^ { 2 } + 3 x > 4$

Describe the right-hand and the left-hand behavior of the graph of $q ( x ) = - 5 x ^ { 4 } + 12 x ^ { 3 } + 13$ .

Find all the zeros of the function. (t - 4)(t - 3)(t - 6i)(t + 6i)

Write the complex conjugate of the complex number.Then multiply the number by its complex conjugate. $\sqrt { - 39 }$

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by $R ( p ) = - 25 p ^ { 2 } + 1900 p$ Where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue.