Question 1

Use synthetic division to divide.​ $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$ ​

Accepted Answer

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

Question 2

Use synthetic division to perform the division.​ $\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }$

Accepted Answer

The answer of Use synthetic division to perform the division.​...

Question 3

Use synthetic division to divide.​ $\frac { x ^ { 3 } + 64 } { x + 4 }$ ​

Accepted Answer

A)  $x ^ { 2 } + 4 x + 16 , x \neq - 4$ 
B)  $x ^ { 2 } - 4 x - 16 , x \neq - 4$ 
C)  $x ^ { 2 } + 4 x - 16 , x \neq - 4$ 
D)  $x ^ { 2 } - 4 x + 16 , x \neq - 4$ 
E) ​ $- x ^ { 2 } + 4 x - 16 , x \neq - 4$ 
A)  $x ^ { 2 } + 4 x + 16 , x \neq - 4$ 
B)  $x ^ { 2 } - 4 x - 16 , x \neq - 4$ 
C)  $x ^ { 2 } + 4 x - 16 , x \neq - 4$ 
D)  $x ^ { 2 } - 4 x + 16 , x \neq - 4$ 
E) ​ $- x ^ { 2 } + 4 x - 16 , x \neq - 4$

Question 4

Use synthetic division to perform the division.​ $\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }$ ​

Accepted Answer

A)  $x ^ { 3 } + x ^ { 2 } + 3 x + 2 - \frac { 11 } { x - 3 }$ 
B)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + \frac { 11 } { x - 3 }$ 
C)  $3 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 2 + \frac { 11 } { x - 3 }$ 
D)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + 11$ 
E) none of these 
A)  $x ^ { 3 } + x ^ { 2 } + 3 x + 2 - \frac { 11 } { x - 3 }$ 
B)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + \frac { 11 } { x - 3 }$ 
C)  $3 x ^ { 3 } - 2 x ^ { 2 } + 6 x - 2 + \frac { 11 } { x - 3 }$ 
D)  $3 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 2 + 11$ 
E) none of these

Question 5

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

Accepted Answer

A) ​ $2 x ^ { 2 } - 5 x + 3$ 
B) ​ $2 x ^ { 2 } - 10 x - 8$ 
C) ​ $2 x ^ { 2 } - x + 12$ 
D) ​ $2 x ^ { 2 } - 6 x + 4$ 
E) ​ $2 x ^ { 2 } + 6 x - 2$ 
A) ​ $2 x ^ { 2 } - 5 x + 3$ 
B) ​ $2 x ^ { 2 } - 10 x - 8$ 
C) ​ $2 x ^ { 2 } - x + 12$ 
D) ​ $2 x ^ { 2 } - 6 x + 4$ 
E) ​ $2 x ^ { 2 } + 6 x - 2$

Question 6

​Use synthetic division to divide. $$\frac { 4 x ^ { 3 } + 31 x ^ { 2 } + 52 x - 15 } { x - \frac { 1 } { 4 } }$$

Accepted Answer

The answer of ​Use synthetic division to divide. \[\frac {...

Question 7

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)  $x ^ { 2 } - 343 x + 49 , x \neq - 7$ 
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)  $x ^ { 2 } - 343 x + 49 , x \neq - 7$ 
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 8

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 9

Simplify the rational expression, $\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }$ ,by using long division or synthetic division.

Accepted Answer

A)  $x ^ { 2 } + 9 x + 20$ 
B)  $x ^ { 2 } + x + 25$ 
C)  $- x ^ { 2 } + 8 x + 25$ 
D)  $$x ^ { 2 } + x - 12$$ 
E)  $- x ^ { 2 } - x + 20$ 
A)  $x ^ { 2 } + 9 x + 20$ 
B)  $x ^ { 2 } + x + 25$ 
C)  $- x ^ { 2 } + 8 x + 25$ 
D)  $$x ^ { 2 } + x - 12$$ 
E)  $- x ^ { 2 } - x + 20$

Question 10

Find all rational roots of the equation. ​
147x 3 - 98x 2 + 27x - 18 = 0
​

Accepted Answer

A)  $x = \frac { 2 } { 5 }$ 
B) ​ $x = \frac { 2 } { 3 }$ 
C) ​ $x = - \frac { 3 } { 7 } i$ 
D) ​ $x = \frac { 3 } { 7 } i$ 
A)  $x = \frac { 2 } { 5 }$ 
B) ​ $x = \frac { 2 } { 3 }$ 
C) ​ $x = - \frac { 3 } { 7 } i$ 
D) ​ $x = \frac { 3 } { 7 } i$

Question 11

Write the function in the form f(x)= (x - k)q(x)+ r for the given value of k and demonstrate that f(k)= r.​ $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Accepted Answer

A)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$ 
B)  $( x + 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
D)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) - 4$ 
E)  $$( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$$ 
A)  $( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$ 
B)  $( x + 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
C)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) + 4$ 
D)  $( x - 4 ) \left( x ^ { 2 } + 3 x - 2 \right) - 4$ 
E)  $$( x - 4 ) \left( x ^ { 2 } - 3 x - 2 \right) + 4$$

Question 12

Find all the rational zeros of the function $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12$ .

Accepted Answer

A) ​x = -2,2,1,3 
B) ​x = 3,1 
C) ​x = -2,-1,-3 
D) ​x = -1,-2 
E) x = -2,2,-1,1,-3 
A) ​x = -2,2,1,3 
B) ​x = 3,1 
C) ​x = -2,-1,-3 
D) ​x = -1,-2 
E) x = -2,2,-1,1,-3

Question 13

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

Accepted Answer

A)  $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$ 
B)  $x ^ { 2 } - x + 1 + \frac { - 5 x + 2 } { x ^ { 2 } + x - 4 }$ 
C)  $x ^ { 2 } - x + 1$ 
D)  $x ^ { 2 } + x - 1$ 
E)  $x ^ { 2 } + x - 1 + \frac { - 5 x - 4 } { x ^ { 2 } + x - 4 }$ 
A)  $x ^ { 2 } - x + 1 - \frac { 4 } { x ^ { 2 } - x + 1 }$ 
B)  $x ^ { 2 } - x + 1 + \frac { - 5 x + 2 } { x ^ { 2 } + x - 4 }$ 
C)  $x ^ { 2 } - x + 1$ 
D)  $x ^ { 2 } + x - 1$ 
E)  $x ^ { 2 } + x - 1 + \frac { - 5 x - 4 } { x ^ { 2 } + x - 4 }$

Question 14

Use long division to divide.​ $\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )$ ​

Accepted Answer

A)  $2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
B)  $2 x ^ { 2 } - 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
C)  $- 2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
D)  $2 x ^ { 2 } + 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
E)  $2 x ^ { 2 } + 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
A)  $2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
B)  $2 x ^ { 2 } - 5 x - 3 , x \neq \frac { 6 } { 3 }$ 
C)  $- 2 x ^ { 2 } - 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
D)  $2 x ^ { 2 } + 5 x + 3 , x \neq \frac { 6 } { 3 }$ 
E)  $2 x ^ { 2 } + 5 x - 3 , x \neq \frac { 6 } { 3 }$

Question 15

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 16

Use synthetic division to divide.​ $\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )$ ​

Accepted Answer

A)  $4 x ^ { 2 } - 8 , x \neq - 6$ 
B)  $4 x ^ { 2 } + 8 , x \neq - 6$ 
C)  $- 4 x ^ { 2 } - 8 , x \neq - 6$ 
D)  $4 x ^ { 3 } - 8 , x \neq - 6$ 
E)  $4 x ^ { 3 } + 8 , x \neq - 6$ 
A)  $4 x ^ { 2 } - 8 , x \neq - 6$ 
B)  $4 x ^ { 2 } + 8 , x \neq - 6$ 
C)  $- 4 x ^ { 2 } - 8 , x \neq - 6$ 
D)  $4 x ^ { 3 } - 8 , x \neq - 6$ 
E)  $4 x ^ { 3 } + 8 , x \neq - 6$

Question 17

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ ,by using long division or synthetic division.

Accepted Answer

A)  $x ^ { 2 } + 7 x + 16$ 
B)  $x ^ { 2 } - 7 x - 12$ 
C)  $x ^ { 2 } - 6 x + 12$ 
D)  $x ^ { 2 } + 8 x + 9$ 
E)  $x ^ { 2 } + x - 12$ 
A)  $x ^ { 2 } + 7 x + 16$ 
B)  $x ^ { 2 } - 7 x - 12$ 
C)  $x ^ { 2 } - 6 x + 12$ 
D)  $x ^ { 2 } + 8 x + 9$ 
E)  $x ^ { 2 } + x - 12$

Question 18

The amounts A (in billions of dollars)donated to support higher education in the United States from 2000 through 2007 are shown in the table,where t represents the year,with t = 0 corresponding to 2000. $$\begin{array} { | c | c | } 
\hline \text { Year, } t & \text { Amount, } A \
\hline 0 & 30.6 \
\hline 1 & 32.3 \
\hline 2 & 34.3 \
\hline 3 & 57.7 \
\hline 4 & 38.1 \
\hline 5 & 42.8 \
\hline 6 & 48 \
\hline 7 & 52.8 \
\hline
\end{array}$$
Use a graphing utility to create a scatter plot of the data.

Accepted Answer

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

Question 19

Write $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28$ in the form f (x)= (x - k)q(x)when k = -3.

Accepted Answer

A)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } + 2 x + 9 \right)$ 
B)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } + 2 x + 9 \right) + 1$ 
C)  $f ( x ) = ( x - 3 ) \left( x ^ { 2 } + 2 x + 9 \right) - 1$ 
D)  $f ( x ) = ( x - 3 ) \left( x ^ { 2 } - 2 x + 9 \right) + 1$ 
E)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } - 2 x + 9 \right) - 1$ 
A)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } + 2 x + 9 \right)$ 
B)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } + 2 x + 9 \right) + 1$ 
C)  $f ( x ) = ( x - 3 ) \left( x ^ { 2 } + 2 x + 9 \right) - 1$ 
D)  $f ( x ) = ( x - 3 ) \left( x ^ { 2 } - 2 x + 9 \right) + 1$ 
E)  $f ( x ) = ( x + 3 ) \left( x ^ { 2 } - 2 x + 9 \right) - 1$

Question 20

Use long division to divide.​ $\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )$ ​

Accepted Answer

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

Exam 13: Polynomial and Synthetic Division

Use synthetic division to divide.​ (5x3+27x2+5x−25)÷(x+5)\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )(5x3+27x2+5x−25)÷(x+5) ​

Use synthetic division to perform the division.​ 3x3+4x2+18x−25x−1\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }x−13x3+4x2+18x−25​

Use synthetic division to divide.​ x3+64x+4\frac { x ^ { 3 } + 64 } { x + 4 }x+4x3+64​ ​

Use synthetic division to perform the division.​ 3x4−7x3−16x+5x−3\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }x−33x4−7x3−16x+5​ ​

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

​Use synthetic division to divide. 4x3+31x2+52x−15x−14\frac { 4 x ^ { 3 } + 31 x ^ { 2 } + 52 x - 15 } { x - \frac { 1 } { 4 } }x−41​4x3+31x2+52x−15​

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

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) ​

Simplify the rational expression, x4+3x3−25x2−39x+180x2−6x+9\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }x2−6x+9x4+3x3−25x2−39x+180​ ,by using long division or synthetic division.

Find all rational roots of the equation. ​ 147x 3 - 98x 2 + 27x - 18 = 0 ​

Write the function in the form f(x)= (x - k)q(x)+ r for the given value of k and demonstrate that f(k)= r.​ f(x)=x3−1x2−14x+12k=4f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4f(x)=x3−1x2−14x+12k=4

Find all the rational zeros of the function f(x)=x5−5x4+11x3−23x2+28x−12f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12f(x)=x5−5x4+11x3−23x2+28x−12 .

Use long division to divide. (x4−4x2−2)÷(x2+x−4)\left( x ^ { 4 } - 4 x ^ { 2 } - 2 \right) \div \left( x ^ { 2 } + x - 4 \right)(x4−4x2−2)÷(x2+x−4)

Use long division to divide.​ (6x3−27x2+39x−18)÷(3x−6)\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )(6x3−27x2+39x−18)÷(3x−6) ​

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

Use synthetic division to divide.​ (4x3−8x+24x2−48)÷(x+6)\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )(4x3−8x+24x2−48)÷(x+6) ​

Simplify the rational expression, 4x3+x2−51x+364x−3\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }4x−34x3+x2−51x+36​ ,by using long division or synthetic division.

Write f(x)=x3+5x2+15x+28f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28f(x)=x3+5x2+15x+28 in the form f (x)= (x - k)q(x)when k = -3.

Use long division to divide.​ (4x3−21x2−33x+28)÷(4x+7)\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )(4x3−21x2−33x+28)÷(4x+7) ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Use synthetic division to divide. $\left( 5 x ^ { 3 } + 27 x ^ { 2 } + 5 x - 25 \right) \div ( x + 5 )$

Use synthetic division to perform the division. $\frac { 3 x ^ { 3 } + 4 x ^ { 2 } + 18 x - 25 } { x - 1 }$

Use synthetic division to divide. $\frac { x ^ { 3 } + 64 } { x + 4 }$

Use synthetic division to perform the division. $\frac { 3 x ^ { 4 } - 7 x ^ { 3 } - 16 x + 5 } { x - 3 }$

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

Use synthetic division to divide. $\frac { 4 x ^ { 3 } + 31 x ^ { 2 } + 52 x - 15 } { x - \frac { 1 } { 4 } }$

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

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

Simplify the rational expression, $\frac { x ^ { 4 } + 3 x ^ { 3 } - 25 x ^ { 2 } - 39 x + 180 } { x ^ { 2 } - 6 x + 9 }$ ,by using long division or synthetic division.

Find all rational roots of the equation. 147x ³ - 98x ² + 27x - 18 = 0

Write the function in the form f(x)= (x - k)q(x)+ r for the given value of k and demonstrate that f(k)= r. $f ( x ) = x ^ { 3 } - 1 x ^ { 2 } - 14 x + 12 \quad k = 4$

Find all the rational zeros of the function $f ( x ) = x ^ { 5 } - 5 x ^ { 4 } + 11 x ^ { 3 } - 23 x ^ { 2 } + 28 x - 12$ .

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

Use long division to divide. $\left( 6 x ^ { 3 } - 27 x ^ { 2 } + 39 x - 18 \right) \div ( 3 x - 6 )$

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

Use synthetic division to divide. $\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )$

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ ,by using long division or synthetic division.

Write $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 15 x + 28$ in the form f (x)= (x - k)q(x)when k = -3.

Use long division to divide. $\left( 4 x ^ { 3 } - 21 x ^ { 2 } - 33 x + 28 \right) \div ( 4 x + 7 )$