Question 1

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 26 }$

Accepted Answer

A)  $- 25 i , 26$ 
B)  $\sqrt { 26 } i , 26$ 
C)  $676 i , 26$ 
D)  $- \sqrt { 26 } i , 26$ 
E)  $- i , 26$

Question 2

Use long division to divide. $\left( 4 x ^ { 3 } - 20 x ^ { 2 } - 52 x + 8 \right) \div ( 4 x + 8 )$

Accepted Answer

A)  $4 x ^ { 2 } - 7 x + 1 , x \neq - 8$ 
B)  $4 x ^ { 2 } + 7 x + 1 , x \neq - 8$ 
C)  $4 x ^ { 2 } - 7 x - 1 , x \neq - 8$ 
D)  $- 4 x ^ { 2 } - 7 x + 1 , x \neq - 8$ 
E)  $4 x ^ { 3 } - 7 x + 1 , x \neq - 8$

Question 3

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 81 - x ^ { 2 } }$

Accepted Answer

A)  $[ - 81,81 ]$ 
B)  $( - 9,9 )$ 
C)  $[ - 9,81 )$ 
D)  $[ - 9,9 ]$ 
E)  $( - 81,81 )$

Question 4

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

Question 5

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$

Accepted Answer

A)  $x = - 3$ 
B)  $x = 3$ 
C)  $x = 0$ 
D)  $x = - 9$ 
E)  $x = 9$

Question 6

Write the quadratic function $f ( x ) = - x ^ { 2 } + 10 x - 18$ in standard form.

Accepted Answer

A)  $f ( x ) = - ( x + 7 ) ^ { 2 } - 5$ 
B)  $f ( x ) = - ( x + 5 ) ^ { 2 } + 7$ 
C)  $f ( x ) = ( x - 5 ) ^ { 2 } - 7$ 
D)  $f ( x ) = - ( x - 5 ) ^ { 2 } + 7$ 
E)  $f ( x ) = ( x - 7 ) ^ { 2 } - 5$

Question 7

Write $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48$ as a product of linear factors.

Accepted Answer

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

Question 8

Find a polynomial function with real coefficients that has the given zeros. $1,3 i$

Accepted Answer

A)  $x ^ { 3 } - x ^ { 2 } - 9 x - 9$ 
B)  $x ^ { 3 } + x ^ { 2 } + 9 x - 9$ 
C)  $x ^ { 3 } - x ^ { 2 } + 9 x - 9$ 
D)  $x ^ { 3 } + x ^ { 2 } + 9 x + 9$ 
E)  $x ^ { 3 } - x ^ { 2 } + 9 x + 9$

Question 9

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Accepted Answer

A)  $0 , \pm \sqrt { 8 }$ 
B)  $0 , \sqrt { 8 }$ 
C)  0,8 
D)  $0 , - 8$ 
E)  $0 , - \sqrt { 8 }$

Question 10

Describe the right-hand and the left-hand behavior of the graph of 
$n ( x ) = - 5 x ^ { 4 } + 10 x ^ { 3 } - 7$

Accepted Answer

A)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. 
B)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
C)  Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.

Question 11

Use long division to divide. $\left( 4 x ^ { 3 } - 8 x ^ { 2 } - 8 x + 12 \right) \div ( 4 x + 4 )$

Accepted Answer

A)  $4 x ^ { 2 } + 3 x + 3 , x \neq - 4$ 
B)  $4 x ^ { 2 } - 3 x + 3 , x \neq - 4$ 
C)  $4 x ^ { 3 } - 3 x + 3 , x \neq - 4$ 
D)  $4 x ^ { 2 } - 3 x - 3 , x \neq - 4$ 
E)  $- 4 x ^ { 2 } - 3 x + 3 , x \neq - 4$

Question 12

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x + 3 }$

Accepted Answer

A)  horizontal: $y = 4$; vertical: $x = - 3$ 
B)  horizontal: $y = 3$; vertical: $x = 0$ 
C)  horizontal: $x = - 3$; vertical: $y = - 4$ 
D)  horizontal: $y = 0$; vertical: $x = - 3$ 
E)  horizontal: $x = 0$; vertical: $y = - 3$

Question 13

Find a polynomial function with real coefficients that has the given zeros. $1,4 i$

Accepted Answer

A)  $x ^ { 3 } + x ^ { 2 } + 16 x + 16$ 
B)  $x ^ { 3 } - x ^ { 2 } + 16 x - 16$ 
C)  $x ^ { 3 } - x ^ { 2 } - 16 x - 16$ 
D)  $x ^ { 3 } - x ^ { 2 } + 16 x + 16$ 
E)  $x ^ { 3 } + x ^ { 2 } + 16 x - 16$

Question 14

Select the correct graph of the function. $$y = x ^ { 5 } - 7 x ^ { 3 } + 3 x$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 15

Use long division to divide. $$\left( 6 x ^ { 3 } - 22 x ^ { 2 } + 15 x - 12 \right) \div ( 3 x - 2 )$$

Accepted Answer

A)  $2 x ^ { 2 } + 6 x - 6 , x \neq - 2$ 
B)  $2 x ^ { 2 } + 6 x + 6 , x \neq - 2$ 
C)  $- 2 x ^ { 2 } - 6 x + 6 , x \neq - 2$ 
D)  $2 x ^ { 2 } - 6 x - 6 , x \neq - 2$ 
E)  $2 x ^ { 2 } - 6 x + 6 , x \neq - 2$

Question 16

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 5 } { x }$

Accepted Answer

A) 
 
B) 
 
C) 
 
D) 
 
E)

Question 17

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

Accepted Answer

A)  $x = - 0.576,1.187,4.388$ 
B)  $x = 5.466$ 
C)  $x = - 4.711$ 
D)  $x = 4.711$ 
E)  $x = - 0.902,0.631,5.271$

Question 18

Perform the addition or subtraction and write the result in standard form. 
$17 i - ( 16 - 8 i )$

Accepted Answer

A)  $16 + 25 i$ 
B)  $- 16 - 25 i$ 
C)  $16 - 25 i$ 
D)  $- 16 + 25 i$ 
E)  $- 16 + 28 i$

Question 19

Write the complex number in standard form. 
$( 3 + \sqrt { - 6 } ) ( 5 - \sqrt { - 14 } )$

Accepted Answer

A)  $( 15 - 2 \sqrt { 21 } ) - ( 5 \sqrt { 6 } - 3 \sqrt { 14 } ) i$ 
B)  $( 15 + 2 \sqrt { 21 } ) + ( 5 \sqrt { 6 } - 3 \sqrt { 14 } ) i$ 
C)  $( 15 - 2 \sqrt { 21 } ) + ( 5 \sqrt { 6 } - 3 \sqrt { 14 } ) i$ 
D)  $( 15 + 2 \sqrt { 21 } ) - ( 5 \sqrt { 6 } - 3 \sqrt { 14 } ) i$ 
E)  $( 15 + 2 \sqrt { 21 } ) + ( 5 \sqrt { 6 } + 3 \sqrt { 14 } ) i$

Question 20

Use synthetic division to divide. 
$\frac { x ^ { 3 } - 216 } { x - 6 }$

Accepted Answer

A)  $x ^ { 2 } + 6 x + 36 , x \neq 6$ 
B)  $x ^ { 2 } + 6 x - 36 , x \neq - 6$ 
C)  $x ^ { 2 } - 6 x + 36 , x \neq - 6$ 
D)  $- x ^ { 2 } + 6 x + 36 , x \neq - 6$ 
E)  $x ^ { 2 } - 6 x - 36 , x \neq - 6$

Exam 2: Polynomial and Rational Functions

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 26 }$

Use long division to divide. $\left( 4 x ^ { 3 } - 20 x ^ { 2 } - 52 x + 8 \right) \div ( 4 x + 8 )$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 81 - x ^ { 2 } }$

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.

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$

Write the quadratic function $f ( x ) = - x ^ { 2 } + 10 x - 18$ in standard form.

Write $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48$ as a product of linear factors.

Find a polynomial function with real coefficients that has the given zeros. $1,3 i$

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - 5 x ^ { 4 } + 10 x ^ { 3 } - 7$

Use long division to divide. $\left( 4 x ^ { 3 } - 8 x ^ { 2 } - 8 x + 12 \right) \div ( 4 x + 4 )$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x + 3 }$

Find a polynomial function with real coefficients that has the given zeros. $1,4 i$

Select the correct graph of the function. $y = x ^ { 5 } - 7 x ^ { 3 } + 3 x$

Use long division to divide. $\left( 6 x ^ { 3 } - 22 x ^ { 2 } + 15 x - 12 \right) \div ( 3 x - 2 )$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 5 } { x }$

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

Perform the addition or subtraction and write the result in standard form. $17 i - ( 16 - 8 i )$

Write the complex number in standard form. $( 3 + \sqrt { - 6 } ) ( 5 - \sqrt { - 14 } )$

Use synthetic division to divide. $\frac { x ^ { 3 } - 216 } { x - 6 }$

Exam 2: Polynomial and Rational Functions

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. −26\sqrt { - 26 }−26​

Use long division to divide. (4x3−20x2−52x+8) ÷(4x+8) \left( 4 x ^ { 3 } - 20 x ^ { 2 } - 52 x + 8 \right) \div ( 4 x + 8 ) (4x3−20x2−52x+8) ÷(4x+8)

Find the domain of xxx in the expression. Use a graphing utility to verify your result. 81−x2\sqrt { 81 - x ^ { 2 } }81−x2​

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.

Find vertical asymptotes of the following function. g(x) =x−3x2−9g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }g(x) =x2−9x−3​

Write the quadratic function f(x) =−x2+10x−18f ( x ) = - x ^ { 2 } + 10 x - 18f(x) =−x2+10x−18 in standard form.

Write f(x) =x3+3x2+16x+48f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48f(x) =x3+3x2+16x+48 as a product of linear factors.

Find a polynomial function with real coefficients that has the given zeros. 1,3i1,3 i1,3i

Find all the real zeros of the polynomial function. f(x) =x5−16x3+64xf ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 xf(x) =x5−16x3+64x

Describe the right-hand and the left-hand behavior of the graph of n(x) =−5x4+10x3−7n ( x ) = - 5 x ^ { 4 } + 10 x ^ { 3 } - 7n(x) =−5x4+10x3−7

Use long division to divide. (4x3−8x2−8x+12) ÷(4x+4) \left( 4 x ^ { 3 } - 8 x ^ { 2 } - 8 x + 12 \right) \div ( 4 x + 4 ) (4x3−8x2−8x+12) ÷(4x+4)

Determine the equations of the vertical and horizontal asymptotes of the graph of the function f(x) =4x+3f ( x ) = \frac { 4 } { x + 3 }f(x) =x+34​

Find a polynomial function with real coefficients that has the given zeros. 1,4i1,4 i1,4i

Select the correct graph of the function. y=x5−7x3+3xy = x ^ { 5 } - 7 x ^ { 3 } + 3 xy=x5−7x3+3x

Use long division to divide. (6x3−22x2+15x−12) ÷(3x−2) \left( 6 x ^ { 3 } - 22 x ^ { 2 } + 15 x - 12 \right) \div ( 3 x - 2 ) (6x3−22x2+15x−12) ÷(3x−2)

Select the correct graph of the following function. f(x) =x2+5xf ( x ) = \frac { x ^ { 2 } + 5 } { x }f(x) =xx2+5​

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

Perform the addition or subtraction and write the result in standard form. 17i−(16−8i) 17 i - ( 16 - 8 i ) 17i−(16−8i)

Write the complex number in standard form. (3+−6) (5−−14) ( 3 + \sqrt { - 6 } ) ( 5 - \sqrt { - 14 } ) (3+−6​) (5−−14​)

Use synthetic division to divide. x3−216x−6\frac { x ^ { 3 } - 216 } { x - 6 }x−6x3−216​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate. $\sqrt { - 26 }$

Use long division to divide. $\left( 4 x ^ { 3 } - 20 x ^ { 2 } - 52 x + 8 \right) \div ( 4 x + 8 )$

Find the domain of $x$ in the expression. Use a graphing utility to verify your result. $\sqrt { 81 - x ^ { 2 } }$

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.

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 3 } { x ^ { 2 } - 9 }$

Write the quadratic function $f ( x ) = - x ^ { 2 } + 10 x - 18$ in standard form.

Write $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 16 x + 48$ as a product of linear factors.

Find a polynomial function with real coefficients that has the given zeros. $1,3 i$

Find all the real zeros of the polynomial function. $f ( x ) = x ^ { 5 } - 16 x ^ { 3 } + 64 x$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - 5 x ^ { 4 } + 10 x ^ { 3 } - 7$

Use long division to divide. $\left( 4 x ^ { 3 } - 8 x ^ { 2 } - 8 x + 12 \right) \div ( 4 x + 4 )$

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 4 } { x + 3 }$

Find a polynomial function with real coefficients that has the given zeros. $1,4 i$

Select the correct graph of the function. $y = x ^ { 5 } - 7 x ^ { 3 } + 3 x$

Use long division to divide. $\left( 6 x ^ { 3 } - 22 x ^ { 2 } + 15 x - 12 \right) \div ( 3 x - 2 )$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 5 } { x }$

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

Perform the addition or subtraction and write the result in standard form. $17 i - ( 16 - 8 i )$

Write the complex number in standard form. $( 3 + \sqrt { - 6 } ) ( 5 - \sqrt { - 14 } )$

Use synthetic division to divide. $\frac { x ^ { 3 } - 216 } { x - 6 }$