Question 1

Perform the operation and write the result in standard form.   $( 4 + 5 i ) ^ { 2 }$

Accepted Answer

A)  $- 9 + 40 i$ 
B)  $- 9 - 40 i$ 
C)  $9 - 40 i$ 
D)  $- 40 + 9 i$ 
E)  $9 + 40 i$ 
A)  $- 9 + 40 i$ 
B)  $- 9 - 40 i$ 
C)  $9 - 40 i$ 
D)  $- 40 + 9 i$ 
E)  $9 + 40 i$

Question 2

Find the zeros (if any) of the rational function.  
  $g ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Accepted Answer

A) -25 
B) ±5 
C) -5 
D) 25 
E) 5 
A) -25 
B) ±5 
C) -5 
D) 25 
E) 5

Question 3

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method.
 $f ( x ) = 5 x ^ { 3 } - 9 x + 8 , f ( 2 )$

Accepted Answer

A) -30 
B) 30 
C) 32 
D) 27 
E) 31 
A) -30 
B) 30 
C) 32 
D) 27 
E) 31

Question 4

Raise the complex number to the fourth power. ​
​4i
​

Accepted Answer

A) ​256 
B) -64 
C) 64 
D) 16 
E) -256 
A) ​256 
B) -64 
C) 64 
D) 16 
E) -256

Question 5

Find all real solutions of the polynomial equation x4 - 7x3 + 42x - 36 = 0.

Accepted Answer

A) x = 1, 6, $\pm \sqrt { 6 }$ 
B) x = 1, 36 
C) x = 1, $\pm \sqrt { 6 }$ 
D) x = 1, -7, -6 
E) x = 1, -36, 12 
A) x = 1, 6, $\pm \sqrt { 6 }$ 
B) x = 1, 36 
C) x = 1, $\pm \sqrt { 6 }$ 
D) x = 1, -7, -6 
E) x = 1, -36, 12

Question 6

Select the correct graph of the following function.   $f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x + 18$

Accepted Answer

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

Question 7

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }$ .

Accepted Answer

A) x-intercept: none; y-intercept: (0, 6) 
B) x-intercept: none; y-intercept: (0, 1) 
C) x-intercept: none; y-intercept: none 
D) x-intercept: (0, 0); y-intercept: (0, 0) 
E) x-intercepts: (-5, 0) and (5, 0); y-intercept: (0, 1) 
A) x-intercept: none; y-intercept: (0, 6) 
B) x-intercept: none; y-intercept: (0, 1) 
C) x-intercept: none; y-intercept: none 
D) x-intercept: (0, 0); y-intercept: (0, 0) 
E) x-intercepts: (-5, 0) and (5, 0); y-intercept: (0, 1)

Question 8

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25$ .

Accepted Answer

A) x = 1, -5, 5, -2 
B) x = -2, -5, -5 
C) x = -1, -5, 5, $\frac { 1 } { 2 }$ 
D)  x = $- \frac { 1 } { 5 }$ , $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ , 5 
E)  x = -2, -5, $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ 
A) x = 1, -5, 5, -2 
B) x = -2, -5, -5 
C) x = -1, -5, 5, $\frac { 1 } { 2 }$ 
D)  x = $- \frac { 1 } { 5 }$ , $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$ , 5 
E)  x = -2, -5, $\frac { 5 } { 2 }$ , $\frac { 1 } { 2 }$

Question 9

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Accepted Answer

A) all real numbers except x = 8 and x = -4 
B) all real numbers 
C) all real numbers except x = 4 and x = -8 
D) all real numbers except x = -4, x = 4 and x = -8 
E) all real numbers except x = -8 
A) all real numbers except x = 8 and x = -4 
B) all real numbers 
C) all real numbers except x = 4 and x = -8 
D) all real numbers except x = -4, x = 4 and x = -8 
E) all real numbers except x = -8

Question 10

Use long division to divide. 
 $8 x ^ { 2 } - 67 x - 45 \div x - 9$

Accepted Answer

A)   $8 x ^ { 2 } + 5 , x \neq 9$ 
B)    $8 x - 5 , x \neq 9$ 
C)   $8 x ^ { 2 } - 5 , x \neq 9$ 
D)   $8 x + 5 , x \neq 9$ 
E)   $8 x + 9 , x \neq 9$ 
A)   $8 x ^ { 2 } + 5 , x \neq 9$ 
B)    $8 x - 5 , x \neq 9$ 
C)   $8 x ^ { 2 } - 5 , x \neq 9$ 
D)   $8 x + 5 , x \neq 9$ 
E)   $8 x + 9 , x \neq 9$

Question 11

Write f(x) = x3 - 5x2 + 16x - 80 as a product of linear factors.

Accepted Answer

A) f(x) = (x - 5)(x - 4)2 
B) f(x) = (x - 5)(x + 4i)(x - 4i) 
C) f(x) = (x - 5)2(x - 4i) 
D) f(x) = (x - 5)(x + 4)2 
E) f(x) = (x + 5)(x - 5)(x + 4) 
A) f(x) = (x - 5)(x - 4)2 
B) f(x) = (x - 5)(x + 4i)(x - 4i) 
C) f(x) = (x - 5)2(x - 4i) 
D) f(x) = (x - 5)(x + 4)2 
E) f(x) = (x + 5)(x - 5)(x + 4)

Question 12

Use Descartes' rule of signs to find the number of possible positive, negative, and nonreal roots for the following equation. 4x 7 + 9x 2 + 5x + 10 = 0

Accepted Answer

A) 0 positive; 1 negative; 6 nonreal 
B) 2 positive; 1 or 3 negative; 4 or 0 nonreal 
C) 0 positive; 0 negative; 7 nonreal 
D) 0 positive; 0 or 2 negative; 5 or 7 nonreal 
E) none of these 
A) 0 positive; 1 negative; 6 nonreal 
B) 2 positive; 1 or 3 negative; 4 or 0 nonreal 
C) 0 positive; 0 negative; 7 nonreal 
D) 0 positive; 0 or 2 negative; 5 or 7 nonreal 
E) none of these

Question 13

Find all the zeros of the function. ​
X(x - 5)2
​

Accepted Answer

A) 0, 5 
B) 1, 5 
C) ±5 
D) 1, -5 
E) 0, -5 
A) 0, 5 
B) 1, 5 
C) ±5 
D) 1, -5 
E) 0, -5

Question 14

Select from the following which is the polynomial of degree n that has the given zero(s).  
Zero
Degree $x = - 7$ $n = 2$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } + 14 x + 49$ 
B)  $f ( x ) = x ^ { 2 } - 14 x - 49$ 
C)  $f ( x ) = - x ^ { 2 } + 14 x + 49$ 
D)  $f ( x ) = x ^ { 2 } - 14 x + 49$ 
E)  $f ( x ) = x ^ { 2 } + 14 x - 49$ 
A)  $f ( x ) = x ^ { 2 } + 14 x + 49$ 
B)  $f ( x ) = x ^ { 2 } - 14 x - 49$ 
C)  $f ( x ) = - x ^ { 2 } + 14 x + 49$ 
D)  $f ( x ) = x ^ { 2 } - 14 x + 49$ 
E)  $f ( x ) = x ^ { 2 } + 14 x - 49$

Question 15

Use the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $v_0$ represents the initial velocity of the object (in feet per second), $s_0$ represents the initial height of the object (in feet), and t represents the time (in seconds). A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of 176 feet per second.At what instant will it be back at ground level?

Accepted Answer

A)  $t = 11$ Sec 
B)  $t = 16$ Sec 
C)  $t = 13$ Sec 
D)  $t = 12$ Sec 
E)  $t = 10$ Sec 
A)  $t = 11$ Sec 
B)  $t = 16$ Sec 
C)  $t = 13$ Sec 
D)  $t = 12$ Sec 
E)  $t = 10$ Sec

Question 16

Find a polynomial function with real coefficients that has the given zeros. ​
6, -6i
​

Accepted Answer

A) x3 - 6x2 - 36x - 216 
B) x3 - 6x2 + 36x + 216 
C) x3 + 6x2 + 36x + 216 
D) x3 - 6x2 + 36x - 216 
E) x3 + 6x2 + 36x - 216 
A) x3 - 6x2 - 36x - 216 
B) x3 - 6x2 + 36x + 216 
C) x3 + 6x2 + 36x + 216 
D) x3 - 6x2 + 36x - 216 
E) x3 + 6x2 + 36x - 216

Question 17

Use long division to divide. 
 $\left( x ^ { 3 } - 343 \right) \div ( x - 7 )$

Accepted Answer

A)   $x ^ { 2 } + 7 x + 49 , x \neq 7$ 
B)  $x ^ { 2 } - 7 x + 49 , x \neq 7$ 
C)  $x ^ { 2 } + 7 x - 49 , x \neq 7$ 
D)  $x ^ { 2 } - 7 x - 49 , x \neq 7$ 
E)  $- x ^ { 2 } + 7 x + 49 , x \neq 7$ 
A)   $x ^ { 2 } + 7 x + 49 , x \neq 7$ 
B)  $x ^ { 2 } - 7 x + 49 , x \neq 7$ 
C)  $x ^ { 2 } + 7 x - 49 , x \neq 7$ 
D)  $x ^ { 2 } - 7 x - 49 , x \neq 7$ 
E)  $- x ^ { 2 } + 7 x + 49 , x \neq 7$

Question 18

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

Accepted Answer

A)  x = -4.692 
B)  x = -8.492, -0.695, 1.186 
C)  x = -3.575 
D)  x = -4.388, -0.720, 1.108 
E)  x = -3.910, -0.763, 1.173 
A)  x = -4.692 
B)  x = -8.492, -0.695, 1.186 
C)  x = -3.575 
D)  x = -4.388, -0.720, 1.108 
E)  x = -3.910, -0.763, 1.173

Question 19

If x = -2 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Accepted Answer

A)  $( x - 5 ) ( x + 2 ) ( x - 2 ) ; x = 5 , - 2,2$ 
B)  $( x + 5 ) ( x + 2 ) ( x - 2 ) ; x = - 5 , - 2,2$ 
C)  $( x + 5 ) ( x + 2 ) ^ { 2 } ; x = - 5 , - 2$ 
D)  $( x + 5 ) ^ { 2 } ( x + 2 ) ; x = - 5 , - 2$ 
E)  $( x + 5 ) ( x - 5 ) ( x - 2 ) ; x = - 5,5,2$ 
A)  $( x - 5 ) ( x + 2 ) ( x - 2 ) ; x = 5 , - 2,2$ 
B)  $( x + 5 ) ( x + 2 ) ( x - 2 ) ; x = - 5 , - 2,2$ 
C)  $( x + 5 ) ( x + 2 ) ^ { 2 } ; x = - 5 , - 2$ 
D)  $( x + 5 ) ^ { 2 } ( x + 2 ) ; x = - 5 , - 2$ 
E)  $( x + 5 ) ( x - 5 ) ( x - 2 ) ; x = - 5,5,2$

Question 20

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .

Accepted Answer

A) x = -2 
B)  $x = - \frac { 9 } { 2 } , x = \frac { 9 } { 2 }$ 
C) x = -81, x = 81 
D) x = -9, x = 9 
E) no zeros 
A) x = -2 
B)  $x = - \frac { 9 } { 2 } , x = \frac { 9 } { 2 }$ 
C) x = -81, x = 81 
D) x = -9, x = 9 
E) no zeros

Perform the operation and write the result in standard form. $( 4 + 5 i ) ^ { 2 }$

Find the zeros (if any) of the rational function. $g ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 5 x ^ { 3 } - 9 x + 8 , f ( 2 )$

Raise the complex number to the fourth power. 4i

Find all real solutions of the polynomial equation x⁴ - 7x³ + 42x - 36 = 0.

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x + 18$

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }$ .

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25$ .

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Use long division to divide. $8 x ^ { 2 } - 67 x - 45 \div x - 9$

Write f(x) = x³ - 5x² + 16x - 80 as a product of linear factors.

Use Descartes' rule of signs to find the number of possible positive, negative, and nonreal roots for the following equation. 4x ⁷ + 9x ² + 5x + 10 = 0

Find all the zeros of the function. X(x - 5)²

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = - 7$ $n = 2$

Find a polynomial function with real coefficients that has the given zeros. 6, -6i

Use long division to divide. $\left( x ^ { 3 } - 343 \right) \div ( x - 7 )$

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

If x = -2 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .

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

Perform the operation and write the result in standard form. (4+5i)2( 4 + 5 i ) ^ { 2 }(4+5i)2

Find the zeros (if any) of the rational function. g(x)=x2−25x+5g ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }g(x)=x+5x2−25​

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. f(x)=5x3−9x+8,f(2)f ( x ) = 5 x ^ { 3 } - 9 x + 8 , f ( 2 )f(x)=5x3−9x+8,f(2)

Raise the complex number to the fourth power. ​ ​4i ​

Find all real solutions of the polynomial equation x4 - 7x3 + 42x - 36 = 0.

Select the correct graph of the following function. f(x)=5x3+4x2−8x+18f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x + 18f(x)=5x3+4x2−8x+18

Identify all intercepts of f(x)=x2x2+25f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }f(x)=x2+25x2​ .

Find all the rational zeros of the function f(x)=−2x4−x3+51x2+25x−25f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25f(x)=−2x4−x3+51x2+25x−25 .

Find the domain of f(x)=x2−16x2+4x−32f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }f(x)=x2+4x−32x2−16​ .

Use long division to divide. 8x2−67x−45÷x−98 x ^ { 2 } - 67 x - 45 \div x - 98x2−67x−45÷x−9

Write f(x) = x3 - 5x2 + 16x - 80 as a product of linear factors.

Use Descartes' rule of signs to find the number of possible positive, negative, and nonreal roots for the following equation. 4x 7 + 9x 2 + 5x + 10 = 0

Find all the zeros of the function. ​ X(x - 5)2 ​

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree x=−7x = - 7x=−7 n=2n = 2n=2

Find a polynomial function with real coefficients that has the given zeros. ​ 6, -6i ​

Use long division to divide. (x3−343)÷(x−7)\left( x ^ { 3 } - 343 \right) \div ( x - 7 )(x3−343)÷(x−7)

Use the zero or root feature of a graphing utility to approximate the zeros of f(x)=2x3+8x2−5x−7f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7f(x)=2x3+8x2−5x−7 accurate to the nearest thousandth.

If x = -2 is a root of x3+5x2−4x−20=0x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 = 0x3+5x2−4x−20=0 , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Determine the zeros (if any) of the rational function f(x)=x2−81x+2f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }f(x)=x+2x2−81​ .

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

Perform the operation and write the result in standard form. $( 4 + 5 i ) ^ { 2 }$

Find the zeros (if any) of the rational function. $g ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

Use the Remainder Theorem and synthetic division to find the function value.Verify your answer using another method. $f ( x ) = 5 x ^ { 3 } - 9 x + 8 , f ( 2 )$

Raise the complex number to the fourth power. 4i

Find all real solutions of the polynomial equation x⁴ - 7x³ + 42x - 36 = 0.

Select the correct graph of the following function. $f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } - 8 x + 18$

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 25 }$ .

Find all the rational zeros of the function $f ( x ) = - 2 x ^ { 4 } - x ^ { 3 } + 51 x ^ { 2 } + 25 x - 25$ .

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Use long division to divide. $8 x ^ { 2 } - 67 x - 45 \div x - 9$

Write f(x) = x³ - 5x² + 16x - 80 as a product of linear factors.

Use Descartes' rule of signs to find the number of possible positive, negative, and nonreal roots for the following equation. 4x ⁷ + 9x ² + 5x + 10 = 0

Find all the zeros of the function. X(x - 5)²

Select from the following which is the polynomial of degree n that has the given zero(s). Zero Degree $x = - 7$ $n = 2$

Find a polynomial function with real coefficients that has the given zeros. 6, -6i

Use long division to divide. $\left( x ^ { 3 } - 343 \right) \div ( x - 7 )$

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

If x = -2 is a root of $x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 81 } { x + 2 }$ .