Question 1

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 5 } { x - 5 }$ 
.

Accepted Answer

$y ( x ) = \frac { 5 } { x - 5 } = \frac { 5 / x } { 1 - 5 / x } \rightarrow 0$ 
as $x \rightarrow \infty$ 
, so $y = 0$ 
is the horizontal asymptote. A vertical asymptote occurs when $x - 5 = 0$ 
or $x = 5$ 
.

Question 2

Find a polynomial of degree 3 with constant coefficient $12$ and zeros $1 / 2$, $- 2$, and $3$

Accepted Answer

A)  $4 x ^ { 3 } - 6 x ^ { 2 } - 22 x - 12$ 
B)  $x ^ { 3 } - 6 x ^ { 2 } - 22 x - 12$ 
C)  $4 x ^ { 3 } - 6 x ^ { 2 } - 22 x + 12$ 
D)  $4 x ^ { 3 } - 6 x ^ { 2 } + 22 x + 12$ 
E)  $4 x ^ { 3 } + 6 x ^ { 2 } - 22 x + 12$ 
A)  $4 x ^ { 3 } - 6 x ^ { 2 } - 22 x - 12$ 
B)  $x ^ { 3 } - 6 x ^ { 2 } - 22 x - 12$ 
C)  $4 x ^ { 3 } - 6 x ^ { 2 } - 22 x + 12$ 
D)  $4 x ^ { 3 } - 6 x ^ { 2 } + 22 x + 12$ 
E)  $4 x ^ { 3 } + 6 x ^ { 2 } - 22 x + 12$ C

Question 3

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$
And $2$, with $2$A double zero

Accepted Answer

A)  $x ^ { 4 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
B)  $x ^ { 4 } + 13 x ^ { 2 } - 4 x ^ { 3 } - 36 x + 36$ 
C)  $x ^ { 4 } + 13 x ^ { 2 } + 4 x ^ { 3 } + 36 x + 36$ 
D)  $4 x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 5 x - 36$ 
A)  $x ^ { 4 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
B)  $x ^ { 4 } + 13 x ^ { 2 } - 4 x ^ { 3 } - 36 x + 36$ 
C)  $x ^ { 4 } + 13 x ^ { 2 } + 4 x ^ { 3 } + 36 x + 36$ 
D)  $4 x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 5 x - 36$ B

Question 4

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Accepted Answer

Positive reals: 4, 2

Question 5

Evaluate the expression and write the result in the form a + bi. $3 i \left( \frac { 1 } { 3 } - i \right)$

Accepted Answer

A)  $\frac { 1 } { 9 } + i$ 
B)  $3 + \frac { i } { 9 }$ 
C)  $i - 3$ 
D)  $3 - i$ 
E)  $3 + i$ 
A)  $\frac { 1 } { 9 } + i$ 
B)  $3 + \frac { i } { 9 }$ 
C)  $i - 3$ 
D)  $3 - i$ 
E)  $3 + i$

Question 6

What is the remainder when the polynomial $p ( x ) = 9 x ^ { 3002 } - 5 x ^ { 3 } + x + 1$ is divided by $( x + 1 )$
?

Accepted Answer

A)  $6$ 
B)  $3001$ 
C)  $- 40$ 
D)  $14$ 
E)  $- 14$ 
A)  $6$ 
B)  $3001$ 
C)  $- 40$ 
D)  $14$ 
E)  $- 14$

Question 7

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$
, $- 2$, and $3$

Accepted Answer

A)  $3 x ^ { 3 } - 21 x - 18$ 
B)  $x ^ { 3 } - 21 x ^ { 2 } - 18$ 
C)  $3 x ^ { 3 } + 21 x + 18$ 
D)  $3 x ^ { 3 } - x ^ { 2 } + 21 x - 18$ 
E)  none 
A)  $3 x ^ { 3 } - 21 x - 18$ 
B)  $x ^ { 3 } - 21 x ^ { 2 } - 18$ 
C)  $3 x ^ { 3 } + 21 x + 18$ 
D)  $3 x ^ { 3 } - x ^ { 2 } + 21 x - 18$ 
E)  none

Question 8

Find the equation of the slant asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }$

Accepted Answer

A)  $y = \frac { 1 } { x - 4 }$ 
B)  $y = 2 x + 2$ 
C)  $x = 2 y + 2$ 
D)  $y = 2 x - 2$ 
E)  $\text { no slant asymptote }$ 
A)  $y = \frac { 1 } { x - 4 }$ 
B)  $y = 2 x + 2$ 
C)  $x = 2 y + 2$ 
D)  $y = 2 x - 2$ 
E)  $\text { no slant asymptote }$

Question 9

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 5 } + 16$ 
by transforming the graph of an appropriate function of the form $y = x ^ { n }$ 
. Indicate all $x$ 
- and $y -$ 
intercepts on your graph.

Accepted Answer

The answer of Sketch the graph of the function \(P...

Question 10

Evaluate the expression $\sqrt { - 10 } \cdot \sqrt { - 40 }$ and write in the form $a + b i$

Accepted Answer

The answer of Evaluate the expression \(\sqrt { - 10...

Question 11

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Accepted Answer

A)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } - x + 3 - \frac { 10 } { x + 3 }$ 
B)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } - x + 2 - \frac { 19 } { x + 3 }$ 
C)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = \frac { x } { 3 } + \frac { 2 x } { 3 } - \frac { 10 } { x + 3 }$ 
D)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } + x + 3 + \frac { 19 } { x + 3 }$ 
E)  none 
A)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } - x + 3 - \frac { 10 } { x + 3 }$ 
B)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } - x + 2 - \frac { 19 } { x + 3 }$ 
C)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = \frac { x } { 3 } + \frac { 2 x } { 3 } - \frac { 10 } { x + 3 }$ 
D)  $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 } = x ^ { 2 } + x + 3 + \frac { 19 } { x + 3 }$ 
E)  none

Question 12

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$

Accepted Answer

A)  zeros: $- 2 , - 1,1,2$ 
B)  zeros: $- 4 , - 1$ 
C)  zeros: $1,2$ 
D)  zeros: $- 2 , - 1,1,0$ 
E)  zeros: $- 1,0,2$ 
A)  zeros: $- 2 , - 1,1,2$ 
B)  zeros: $- 4 , - 1$ 
C)  zeros: $1,2$ 
D)  zeros: $- 2 , - 1,1,0$ 
E)  zeros: $- 1,0,2$

Question 13

Use a graphing device to graph the polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

Accepted Answer

A)  $p ( x ) \rightarrow 0$ As $x \rightarrow \infty$ 
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $ 
B)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty 3$ 
C)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
D)  $p ( x ) \rightarrow - 1$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
E)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty$ 
A)  $p ( x ) \rightarrow 0$ As $x \rightarrow \infty$ 
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $ 
B)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty 3$ 
C)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
D)  $p ( x ) \rightarrow - 1$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
E)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty$

Question 14

Find the complete factorization of $P ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 1$

Accepted Answer

The answer of Find the complete factorization of \(P (...

Question 15

What is the remainder when the polynomial $p ( x ) = 6 x ^ { 300 } + x ^ { 63 } - 2 x ^ { 2 } - x + 20$ 
is divided by $( x + 1 )$ 
?

Accepted Answer

If @#LAT-DLM& 
is di

Question 16

Evaluate the expression and write in the form $a + b i$ . $i ^ { 37 }$

Accepted Answer

The answer of Evaluate the expression and write in the...

Question 17

Find a polynomial of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of $x ^ { 2 }$ is -5.

Accepted Answer

The answer of Find a polynomial of degree 3 that...

Question 18

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

Accepted Answer

A)  $x ^ { 4 } ( x - \sqrt { 3 } ) ^ { 2 }$ 
B)  $x ^ { 2 } ( x - 3 ) ^ { 2 } ( x + 3 ) ^ { 2 }$ 
C)  $x ^ { 2 } \left( x ^ { 4 } - 6 x ^ { 2 } - 9 \right)$ 
D)  $x ^ { 4 } ( x + 9 ) ^ { 2 }$ 
E)  none 
A)  $x ^ { 4 } ( x - \sqrt { 3 } ) ^ { 2 }$ 
B)  $x ^ { 2 } ( x - 3 ) ^ { 2 } ( x + 3 ) ^ { 2 }$ 
C)  $x ^ { 2 } \left( x ^ { 4 } - 6 x ^ { 2 } - 9 \right)$ 
D)  $x ^ { 4 } ( x + 9 ) ^ { 2 }$ 
E)  none

Question 19

Find all zeros. $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Accepted Answer

A)  $\{ - 1,1,4 \}$ 
B)  $\{ 4 , - i , i \}$ 
C)  $\{ 2,1 - i , 1 + i \}$ 
D)  $\{ - 4 , - 1 - i , - 1 + i \}$ 
E)  none of these 
A)  $\{ - 1,1,4 \}$ 
B)  $\{ 4 , - i , i \}$ 
C)  $\{ 2,1 - i , 1 + i \}$ 
D)  $\{ - 4 , - 1 - i , - 1 + i \}$ 
E)  none of these

Question 20

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

Accepted Answer

The answer of Factor the polynomial completely. \(p ( x...

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 5 } { x - 5 }$ .

Find a polynomial of degree 3 with constant coefficient $12$ and zeros $1 / 2$ , $- 2$ , and $3$

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ And $2$ , with $2$ A double zero

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Evaluate the expression and write the result in the form a + bi. $3 i \left( \frac { 1 } { 3 } - i \right)$

What is the remainder when the polynomial $p ( x ) = 9 x ^ { 3002 } - 5 x ^ { 3 } + x + 1$ is divided by $( x + 1 )$ ?

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$ , $- 2$ , and $3$

Find the equation of the slant asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }$

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 5 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ . Indicate all $x$ - and $y -$ intercepts on your graph.

Evaluate the expression $\sqrt { - 10 } \cdot \sqrt { - 40 }$ and write in the form $a + b i$

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$

Use a graphing device to graph the polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

Find the complete factorization of $P ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 1$

What is the remainder when the polynomial $p ( x ) = 6 x ^ { 300 } + x ^ { 63 } - 2 x ^ { 2 } - x + 20$ is divided by $( x + 1 )$ ?

Evaluate the expression and write in the form $a + b i$ . $i ^ { 37 }$

Find a polynomial of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of $x ^ { 2 }$ is -5.

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

Find all zeros. $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 4: Exponential and Logarithmic Functions

Find all horizontal and vertical asymptotes of the function y(x)=5x−5y ( x ) = \frac { 5 } { x - 5 }y(x)=x−55​ .

Find a polynomial of degree 3 with constant coefficient 121212 and zeros 1/21 / 21/2 , −2- 2−2 , and 333

Find a polynomial of degree 444 , with integer coefficients that has zeros of 3i3 i3i And 222 , with 222 A double zero

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. p(x)=x5−4x4−13x3+70x2−90x+36p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36p(x)=x5−4x4−13x3+70x2−90x+36

Evaluate the expression and write the result in the form a + bi. 3i(13−i)3 i \left( \frac { 1 } { 3 } - i \right)3i(31​−i)

What is the remainder when the polynomial p(x)=9x3002−5x3+x+1p ( x ) = 9 x ^ { 3002 } - 5 x ^ { 3 } + x + 1p(x)=9x3002−5x3+x+1 is divided by (x+1)( x + 1 )(x+1) ?

Find a polynomial of degree 3 with constant coefficient −18- 18−18 and zeros −1- 1−1 , −2- 2−2 , and 333

Find the equation of the slant asymptote, if any. r(x)=2x2−6x−7x−4r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }r(x)=x−42x2−6x−7​

Sketch the graph of the function P(x)=(x−1)5+16P ( x ) = ( x - 1 ) ^ { 5 } + 16P(x)=(x−1)5+16 by transforming the graph of an appropriate function of the form y=xny = x ^ { n }y=xn . Indicate all xxx - and y−y -y− intercepts on your graph.

Evaluate the expression −10⋅−40\sqrt { - 10 } \cdot \sqrt { - 40 }−10​⋅−40​ and write in the form a+bia + b ia+bi

Divide. x3+2x2−10x+3\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }x+3x3+2x2−10​

Sketch the graph of PPP to find all real zeros. P(x)=x4−5x2+4P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4P(x)=x4−5x2+4

Use a graphing device to graph the polynomial p(x)=−x5−4x3−10xp ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 xp(x)=−x5−4x3−10x to describe its end behavior

Find the complete factorization of P(x)=x4+2x3+2x2+2x+1P ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 1P(x)=x4+2x3+2x2+2x+1

What is the remainder when the polynomial p(x)=6x300+x63−2x2−x+20p ( x ) = 6 x ^ { 300 } + x ^ { 63 } - 2 x ^ { 2 } - x + 20p(x)=6x300+x63−2x2−x+20 is divided by (x+1)( x + 1 )(x+1) ?

Evaluate the expression and write in the form a+bia + b ia+bi . i37i ^ { 37 }i37

Find a polynomial of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of x2x ^ { 2 }x2 is -5.

Factor the polynomial completely. p(x)=x6−6x4+9x2p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }p(x)=x6−6x4+9x2

Find all zeros. P(x)=x3−2x2−6x−8P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8P(x)=x3−2x2−6x−8

Factor the polynomial completely. p(x)=x6−6x4+9x2p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }p(x)=x6−6x4+9x2

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 5 } { x - 5 }$ .

Find a polynomial of degree 3 with constant coefficient $12$ and zeros $1 / 2$ , $- 2$ , and $3$

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ And $2$ , with $2$ A double zero

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Evaluate the expression and write the result in the form a + bi. $3 i \left( \frac { 1 } { 3 } - i \right)$

What is the remainder when the polynomial $p ( x ) = 9 x ^ { 3002 } - 5 x ^ { 3 } + x + 1$ is divided by $( x + 1 )$ ?

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$ , $- 2$ , and $3$

Find the equation of the slant asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }$

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 5 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ . Indicate all $x$ - and $y -$ intercepts on your graph.

Evaluate the expression $\sqrt { - 10 } \cdot \sqrt { - 40 }$ and write in the form $a + b i$

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 5 x ^ { 2 } + 4$

Use a graphing device to graph the polynomial $p ( x ) = - x ^ { 5 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

Find the complete factorization of $P ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x + 1$

What is the remainder when the polynomial $p ( x ) = 6 x ^ { 300 } + x ^ { 63 } - 2 x ^ { 2 } - x + 20$ is divided by $( x + 1 )$ ?

Evaluate the expression and write in the form $a + b i$ . $i ^ { 37 }$

Find a polynomial of degree 3 that has zeros 1, -2, and 3 and in which the coefficient of $x ^ { 2 }$ is -5.

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$

Find all zeros. $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Factor the polynomial completely. $p ( x ) = x ^ { 6 } - 6 x ^ { 4 } + 9 x ^ { 2 }$