Question 1

Determine whether the given constant is a solution to the given polynomial equation.
-$x ^ { 4 } - 3 x ^ { 2 } - 4 = 0 ; - 1$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 2

Find the cubic or quartic function that models the data in the table.
-$\begin{array}{c|cccc}
x & -3 & 1 & 3 & 4 \
\hline y & 50 & -3 & -45 & -102
\end{array} \text { (Cubic) }$

Accepted Answer

A)  $y = - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
B)  $y = - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$ 
C)  $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
D)  $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$ 
A)  $y = - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
B)  $y = - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$ 
C)  $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
D)  $y = - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$

Question 3

Use synthetic division to find the quotient and remainder.
-$$\left( x ^ { 4 } - 2 \right) \div ( x - 3 )$$

Accepted Answer

A)  $x ^ { 3 } + 7 x ^ { 2 } + 6 x + 3 + \frac { 79 } { x - 3 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 13 } { x - 3 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 13 } { x - 3 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 79 } { x - 3 }$ 
A)  $x ^ { 3 } + 7 x ^ { 2 } + 6 x + 3 + \frac { 79 } { x - 3 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 13 } { x - 3 }$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 13 } { x - 3 }$ 
D)  $x ^ { 3 } + 3 x ^ { 2 } + 9 x + 27 + \frac { 79 } { x - 3 }$

Question 4

$\frac { 5 } { x + 6 } \geq \frac { 1 } { x - 1 }$

Accepted Answer

A)  $- 1  \frac { 11 } { 4 }$ 
B)  $- 6 < x < 1 \text { or } x \geq \frac { 11 } { 4 }$ 
C)  $- 6 \leq x \leq 1 \text { or } x \geq \frac { 11 } { 4 }$ 
D)  $- 1 \leq x \leq 6 \text { or } x \geq \frac { 11 } { 4 }$ 
A)  $- 1  \frac { 11 } { 4 }$ 
B)  $- 6 < x < 1 \text { or } x \geq \frac { 11 } { 4 }$ 
C)  $- 6 \leq x \leq 1 \text { or } x \geq \frac { 11 } { 4 }$ 
D)  $- 1 \leq x \leq 6 \text { or } x \geq \frac { 11 } { 4 }$

Question 5

Solve the polynomial equation by using the root method.
-$$\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$$

Accepted Answer

A)  $2 , - 2$ 
B)  $- 2$ 
C)  2,0 
D)  2 
A)  $2 , - 2$ 
B)  $- 2$ 
C)  2,0 
D)  2

Question 6

$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$

Accepted Answer

A)   1,-1,7 
B)  $- \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$ 
C)   2,-2,7 
D)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$ 
A)   1,-1,7 
B)  $- \frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$ 
C)   2,-2,7 
D)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 7$

Question 7

Graph the function.
-$$f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }$$

Accepted Answer

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

Question 8

$f ( x ) = 0.3 x ^ { 5 } + 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } + 2$

Accepted Answer

A)   [-5000,5000]  by  [-150,150] 
B)   [-10,10]  by  [-1200,2000] 
C)   [-6,6]  by  [-3000,3000] 
D)   [-20,20]  by  [-5000,8000] 
A)   [-5000,5000]  by  [-150,150] 
B)   [-10,10]  by  [-1200,2000] 
C)   [-6,6]  by  [-3000,3000] 
D)   [-20,20]  by  [-5000,8000]

Question 9

Use algebraic and/or graphical methods to solve the inequality.
-$$( x + 10 ) \left( x ^ { 2 } - 49 \right) > 0$$

Accepted Answer

A)  $x  7$ 
D)  $- 10  7$ 
A)  $x  7$ 
D)  $- 10  7$

Question 10

Use analytical methods to solve the equation.
-x x $$\frac { + 2 } { - 2 } = 9$$

Accepted Answer

A)  No solution 
B)  $- \frac { 8 } { 5 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  2 
A)  No solution 
B)  $- \frac { 8 } { 5 }$ 
C)  $\frac { 5 } { 2 }$ 
D)  2

Question 11

Find one solution graphically and then find the remaining solutions using synthetic division.
-$$6 x ^ { 3 } + 22 x ^ { 2 } + 10 x - 6 = 0$$

Accepted Answer

A)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , - 3$ 
B)  $- 1 , - 3 , \frac { 1 } { 3 }$ 
C)  $- 1 , \frac { 1 } { 3 } , 3$ 
D)  $- \frac { 1 } { 3 } , - 3 , \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 3 } , \frac { 1 } { 3 } , - 3$ 
B)  $- 1 , - 3 , \frac { 1 } { 3 }$ 
C)  $- 1 , \frac { 1 } { 3 } , 3$ 
D)  $- \frac { 1 } { 3 } , - 3 , \frac { 1 } { 3 }$

Question 12

Match the function with its graph.
-$$f ( x ) = \frac { x ^ { 2 } + 4 x } { x - 1 }$$

Accepted Answer

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

Question 13

Provide an appropriate response.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 112,500 } { x + 225 }$. What is the cost per ton for $x = 20$ ?

Accepted Answer

A)  $25.00 
B)  $5625.00 
C)  $5400.00 
D)  $459.18 
A)  $25.00 
B)  $5625.00 
C)  $5400.00 
D)  $459.18

Question 14

$F(x)=\frac{-1}{(x+1)^{2}}$

Accepted Answer

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

Question 15

Solve the equation exactly in the complex number system.
-$$x ^ { 3 } + 7 x ^ { 2 } + 25 x + 175 = 0$$

Accepted Answer

A)  $x = - 7 , x = \pm 5 i$ 
B)  $x = - 5 i , x = \pm 7 i$ 
C)  $x = - 7 i , x = \pm 5 i$ 
D)  $x = - 5 , x = \pm 7 i$ 
A)  $x = - 7 , x = \pm 5 i$ 
B)  $x = - 5 i , x = \pm 7 i$ 
C)  $x = - 7 i , x = \pm 5 i$ 
D)  $x = - 5 , x = \pm 7 i$

Question 16

For the given rational function, find all values of x for which y has the indicated value.
-y = x x -- 3 5 ; y = 13

Accepted Answer

A)  2 
B)  12 
C)  - 12 
D)  -2 
A)  2 
B)  12 
C)  - 12 
D)  -2

Question 17

Determine all possible rational solutions of the polynomial equation.
-$$f ( x ) = 3 x ^ { 3 } + 58 x ^ { 2 } + 58 x + 27$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
B)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
D)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$ 
A)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 27 } , \pm 3$ 
B)  $\pm 1 , \pm \frac { 1 } { 3 } , \pm 3 , \pm 9 , \pm 27$ 
C)  $\pm 1 , \pm 3 , \pm 6 , \pm 9 , \pm 27$ 
D)  $\pm 1 , \pm 3 , \pm 9 , \pm 27$

Question 18

Solve the equation exactly in the complex number system.
-$6 x ^ { 3 } + 6 x = 0$

Accepted Answer

A)  $x = - 6 , x = \pm i$ 
B)  $x = 0 , x = \pm i$ 
C)  $x = \pm i$ 
D)  $x = 0 , x = \pm 1$ 
A)  $x = - 6 , x = \pm i$ 
B)  $x = 0 , x = \pm i$ 
C)  $x = \pm i$ 
D)  $x = 0 , x = \pm 1$

Question 19

Match the function with its graph.
-$$f ( x ) = \frac { 1 } { x + 5 }$$

Accepted Answer

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

Question 20

Determine whether the second polynomial is a factor of the first polynomial.
-$$\left( 7 x ^ { 3 } + 24 x ^ { 2 } - 17 x + 4 \right) ; ( x + 4 )$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Determine whether the given constant is a solution to the given polynomial equation. - $x ^ { 4 } - 3 x ^ { 2 } - 4 = 0 ; - 1$

Find the cubic or quartic function that models the data in the table. - x -3 1 3 4 y 50 -3 -45 -102 start text left parenthesisCubicright parenthesis end text

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 4 } - 2 \right) \div ( x - 3 )$

$\frac { 5 } { x + 6 } \geq \frac { 1 } { x - 1 }$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$

$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }$

$f ( x ) = 0.3 x ^ { 5 } + 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } + 2$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 10 ) \left( x ^ { 2 } - 49 \right) > 0$

Use analytical methods to solve the equation. -x x $\frac { + 2 } { - 2 } = 9$

Find one solution graphically and then find the remaining solutions using synthetic division. - $6 x ^ { 3 } + 22 x ^ { 2 } + 10 x - 6 = 0$

Match the function with its graph. - $f ( x ) = \frac { x ^ { 2 } + 4 x } { x - 1 }$

Provide an appropriate response. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 20$ ?

$F(x)=\frac{-1}{(x+1)^{2}}$

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 7 x ^ { 2 } + 25 x + 175 = 0$

For the given rational function, find all values of x for which y has the indicated value. -y = x x -- 3 5 ; y = 13

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = 3 x ^ { 3 } + 58 x ^ { 2 } + 58 x + 27$

Solve the equation exactly in the complex number system. - $6 x ^ { 3 } + 6 x = 0$

Match the function with its graph. - $f ( x ) = \frac { 1 } { x + 5 }$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 7 x ^ { 3 } + 24 x ^ { 2 } - 17 x + 4 \right) ; ( x + 4 )$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 6: Higher-Degree Polynomial and Rational Functions

Determine whether the given constant is a solution to the given polynomial equation. - x4−3x2−4=0;−1x ^ { 4 } - 3 x ^ { 2 } - 4 = 0 ; - 1x4−3x2−4=0;−1

Find the cubic or quartic function that models the data in the table. - x -3 1 3 4 y 50 -3 -45 -102 start text left parenthesisCubicright parenthesis end text

Use synthetic division to find the quotient and remainder. - (x4−2)÷(x−3)\left( x ^ { 4 } - 2 \right) \div ( x - 3 )(x4−2)÷(x−3)

5x+6≥1x−1\frac { 5 } { x + 6 } \geq \frac { 1 } { x - 1 }x+65​≥x−11​

Solve the polynomial equation by using the root method. - 12x3+4=0\frac { 1 } { 2 } x ^ { 3 } + 4 = 021​x3+4=0

4x3−28x2−x+7=04 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 04x3−28x2−x+7=0

Graph the function. - f(x)=x2+x−9x2−9f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }f(x)=x2−9x2+x−9​

f(x)=0.3x5+3x4−2x3+3x2+2f ( x ) = 0.3 x ^ { 5 } + 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } + 2f(x)=0.3x5+3x4−2x3+3x2+2

Use algebraic and/or graphical methods to solve the inequality. - (x+10)(x2−49)>0( x + 10 ) \left( x ^ { 2 } - 49 \right) > 0(x+10)(x2−49)>0

Use analytical methods to solve the equation. -x x +2−2=9\frac { + 2 } { - 2 } = 9−2+2​=9

Find one solution graphically and then find the remaining solutions using synthetic division. - 6x3+22x2+10x−6=06 x ^ { 3 } + 22 x ^ { 2 } + 10 x - 6 = 06x3+22x2+10x−6=0

Match the function with its graph. - f(x)=x2+4xx−1f ( x ) = \frac { x ^ { 2 } + 4 x } { x - 1 }f(x)=x−1x2+4x​

Provide an appropriate response. -Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by y=112,500x+225y = \frac { 112,500 } { x + 225 }y=x+225112,500​ . What is the cost per ton for x=20x = 20x=20 ?

F(x)=−1(x+1)2F(x)=\frac{-1}{(x+1)^{2}}F(x)=(x+1)2−1​

Solve the equation exactly in the complex number system. - x3+7x2+25x+175=0x ^ { 3 } + 7 x ^ { 2 } + 25 x + 175 = 0x3+7x2+25x+175=0

For the given rational function, find all values of x for which y has the indicated value. -y = x x -- 3 5 ; y = 13

Determine all possible rational solutions of the polynomial equation. - f(x)=3x3+58x2+58x+27f ( x ) = 3 x ^ { 3 } + 58 x ^ { 2 } + 58 x + 27f(x)=3x3+58x2+58x+27

Solve the equation exactly in the complex number system. - 6x3+6x=06 x ^ { 3 } + 6 x = 06x3+6x=0

Match the function with its graph. - f(x)=1x+5f ( x ) = \frac { 1 } { x + 5 }f(x)=x+51​

Determine whether the second polynomial is a factor of the first polynomial. - (7x3+24x2−17x+4);(x+4)\left( 7 x ^ { 3 } + 24 x ^ { 2 } - 17 x + 4 \right) ; ( x + 4 )(7x3+24x2−17x+4);(x+4)

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Determine whether the given constant is a solution to the given polynomial equation. - $x ^ { 4 } - 3 x ^ { 2 } - 4 = 0 ; - 1$

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 4 } - 2 \right) \div ( x - 3 )$

$\frac { 5 } { x + 6 } \geq \frac { 1 } { x - 1 }$

Solve the polynomial equation by using the root method. - $\frac { 1 } { 2 } x ^ { 3 } + 4 = 0$

$4 x ^ { 3 } - 28 x ^ { 2 } - x + 7 = 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 9 }$

$f ( x ) = 0.3 x ^ { 5 } + 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } + 2$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 10 ) \left( x ^ { 2 } - 49 \right) > 0$

Use analytical methods to solve the equation. -x x $\frac { + 2 } { - 2 } = 9$

Find one solution graphically and then find the remaining solutions using synthetic division. - $6 x ^ { 3 } + 22 x ^ { 2 } + 10 x - 6 = 0$

Match the function with its graph. - $f ( x ) = \frac { x ^ { 2 } + 4 x } { x - 1 }$

Provide an appropriate response. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 112,500 } { x + 225 }$ . What is the cost per ton for $x = 20$ ?

$F(x)=\frac{-1}{(x+1)^{2}}$

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 7 x ^ { 2 } + 25 x + 175 = 0$

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = 3 x ^ { 3 } + 58 x ^ { 2 } + 58 x + 27$

Solve the equation exactly in the complex number system. - $6 x ^ { 3 } + 6 x = 0$

Match the function with its graph. - $f ( x ) = \frac { 1 } { x + 5 }$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 7 x ^ { 3 } + 24 x ^ { 2 } - 17 x + 4 \right) ; ( x + 4 )$