Question 1

Find one solution graphically and then find the remaining solutions using synthetic division.
-$$2 x ^ { 3 } + 5 x ^ { 2 } - 14 x - 8 = 0$$

Accepted Answer

A)  $4 , - 2,1$ 
B)  $- 4,2 , - 1 / 2$ 
C)  $- 4,2 , - 1$ 
D)  $4 , - 2,1 / 2$ 
A)  $4 , - 2,1$ 
B)  $- 4,2 , - 1 / 2$ 
C)  $- 4,2 , - 1$ 
D)  $4 , - 2,1 / 2$

Question 2

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions.
-$$6 x ^ { 3 } + 16 x ^ { 2 } + 6 x - 4 = 0 ; - 1$$

Accepted Answer

A)  $\frac { 1 } { 3 } , 2$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 }$ 
C)  $- 2 , \frac { 1 } { 3 }$ 
D)  $\pm \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 3 } , 2$ 
B)  $\frac { 1 } { 3 } , \frac { 1 } { 3 }$ 
C)  $- 2 , \frac { 1 } { 3 }$ 
D)  $\pm \frac { 1 } { 3 }$

Question 3

Determine whether the second polynomial is a factor of the first polynomial.
-$\left( 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 \right) ; ( x + 2 )$

Accepted Answer

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

Question 4

Provide an appropriate response.
-If $y$ varies inversely as the 4 th power of $x$ and $y = 8$ when $x = - 2$, what is $y$ when $x = 0.5$ ?

Accepted Answer

A)  128 
B)  $- 2048$ 
C)  2048 
D)  8 
A)  128 
B)  $- 2048$ 
C)  2048 
D)  8

Question 5

Use factoring and the root method to solve the polynomial equation.
-$0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$

Accepted Answer

A)  $- 3 \sqrt { 10 } , 0,3 \sqrt { 10 }$ 
B)  $- 9 \sqrt { 10 } , 0,9 \sqrt { 10 }$ 
C)  $0,3 \sqrt { 10 }$ 
D)  $- 9 \sqrt { 10 } , 9 \sqrt { 10 }$ 
A)  $- 3 \sqrt { 10 } , 0,3 \sqrt { 10 }$ 
B)  $- 9 \sqrt { 10 } , 0,9 \sqrt { 10 }$ 
C)  $0,3 \sqrt { 10 }$ 
D)  $- 9 \sqrt { 10 } , 9 \sqrt { 10 }$

Question 6

Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }$$

Accepted Answer

A)  $y = 3 , y = - 7$ 
B)  $x = 3 , x = - 7$ 
C)  $y = 6$ 
D)  $x = - 3 , x = 7$ 
A)  $y = 3 , y = - 7$ 
B)  $x = 3 , x = - 7$ 
C)  $y = 6$ 
D)  $x = - 3 , x = 7$

Question 7

Provide an appropriate response.
-Which function has no vertical asymptote? Why? a. $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$
b. $f ( x ) = \frac { 2 } { x ^ { 2 } - 6 x }$
c. $f ( x ) = \frac { 3 x ^ { 2 } + 15 } { x ^ { 2 } + 6 }$
d. $f ( x ) = \frac { x + 5 } { ( x - 5 ) ( x - 3 ) }$

Accepted Answer

A)  b. The numerator is never equal to 0. 
B)  d. No factor from the denominator cancels out. 
C)  a. The degree of the denominator is larger than the degree of the numerator. 
D)  c. The denominator is never equal to 0. 
A)  b. The numerator is never equal to 0. 
B)  d. No factor from the denominator cancels out. 
C)  a. The degree of the denominator is larger than the degree of the numerator. 
D)  c. The denominator is never equal to 0.

Question 8

Determine whether the given constant is a solution to the given polynomial equation.
-$7 x ^ { 3 } - 2 x ^ { 2 } + x - 6 = 0 ; 1$

Accepted Answer

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

Question 9

Give the equations of any horizontal asymptotes for the graphs of the rational functions.
-$$h ( x ) = \frac { 2 x ^ { 2 } - 8 x - 7 } { 9 x ^ { 2 } - 3 x + 8 }$$

Accepted Answer

A)  none 
B)  $y = \frac { 2 } { 9 }$ 
C)  $y = \frac { 8 } { 3 }$ 
D)  $y = 0$ 
A)  none 
B)  $y = \frac { 2 } { 9 }$ 
C)  $y = \frac { 8 } { 3 }$ 
D)  $y = 0$

Question 10

Predict the end behavior of the graph of the function.
-$$f ( x ) = 9 ( x - 2 ) \left( x ^ { 2 } + 2 \right)$$

Accepted Answer

A)  Down on both sides 
B)  Up on both sides 
C)  Down on the right side, up on the left side 
D)  Up on the right side, down on the left side 
A)  Down on both sides 
B)  Up on both sides 
C)  Down on the right side, up on the left side 
D)  Up on the right side, down on the left side

Question 11

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic.
-

Accepted Answer

A)  Positive; Cubic 
B)  Negative; Quartic 
C)  Positive; Quartic 
D)  Negative; Cubic 
A)  Positive; Cubic 
B)  Negative; Quartic 
C)  Positive; Quartic 
D)  Negative; Cubic

Question 12

Solve the polynomial equation by factoring.
-$$2 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 0$$

Accepted Answer

A)  $- 1,1 , - 2$ 
B)  $1 , - 2$ 
C)  $1 , - 1,2$ 
D)  $- 1 , - 2$ 
A)  $- 1,1 , - 2$ 
B)  $1 , - 2$ 
C)  $1 , - 1,2$ 
D)  $- 1 , - 2$

Question 13

Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$h ( x ) = \frac { ( x - 6 ) ( x + 1 ) } { x ^ { 2 } - 4 }$$

Accepted Answer

A)  $x = - 6 , x = 1$ 
B)  $x = 2 , x = - 2$ 
C)  $x = 6 , x = - 1$ 
D)  none 
A)  $x = - 6 , x = 1$ 
B)  $x = 2 , x = - 2$ 
C)  $x = 6 , x = - 1$ 
D)  none

Question 14

Use synthetic division to find the quotient and remainder.
-$$\left( x ^ { 3 } - 1 \right) \div ( x - 1 )$$

Accepted Answer

A)  $x ^ { 3 } + x ^ { 2 } + x + 1$ 
B)  $x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } + x + 1$ 
D)  $x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
A)  $x ^ { 3 } + x ^ { 2 } + x + 1$ 
B)  $x ^ { 3 } + x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } + x + 1$ 
D)  $x ^ { 2 } + x + 1 + \frac { 1 } { x - 1 }$

Question 15

Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { x - 7 } { x ^ { 2 } - 9 }$$

Accepted Answer

A)  $x = 7$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $x = 3 , x = - 3$ 
A)  $x = 7$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  $x = 3 , x = - 3$

Question 16

Find the cubic or quartic function that models the data in the table.
-$\begin{array}{l|lccc}
x & -2 & 0 & 1 & 3 \
\hline y & 10 & 15 & 21 & 33
\end{array} \text { (Cubic) }$

Accepted Answer

A)  $y = - 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.10 x + 15.00$ 
B)  $y = 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.30 x + 15.00$ 
C)  $y = 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.10 x + 15.00$ 
D)  $y = - 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.30 x + 15.00$ 
A)  $y = - 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.10 x + 15.00$ 
B)  $y = 0.23 x ^ { 3 } + 0.73 x ^ { 2 } + 5.30 x + 15.00$ 
C)  $y = 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.10 x + 15.00$ 
D)  $y = - 0.23 x ^ { 3 } + 0.93 x ^ { 2 } + 5.30 x + 15.00$

Question 17

Solve the polynomial equation by factoring.
-$$x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 = 0$$

Accepted Answer

A)  $- 3 , - 4,2$ 
B)  $- 2 , - 3,0$ 
C)  $3,4 , - 2$ 
D)  $2,3 , - 2$ 
A)  $- 3 , - 4,2$ 
B)  $- 2 , - 3,0$ 
C)  $3,4 , - 2$ 
D)  $2,3 , - 2$

Question 18

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$

Accepted Answer

A)  16,2 
B)  16, $\pm \sqrt { 2 }$ 
C)  4, $\sqrt { 2 }$ 
D)  $\pm 4 , \pm \sqrt { 2 }$ 
A)  16,2 
B)  16, $\pm \sqrt { 2 }$ 
C)  4, $\sqrt { 2 }$ 
D)  $\pm 4 , \pm \sqrt { 2 }$

Question 19

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-

Accepted Answer

A)  $- 6 , - 2,4$ 
B)  2,4 
C)  $- 6 , - 2$ 
D)  $- 4,2,6$ 
A)  $- 6 , - 2,4$ 
B)  2,4 
C)  $- 6 , - 2$ 
D)  $- 4,2,6$

Question 20

State the degree and leading coefficient of the polynomial function.
-$$f ( x ) = 19 + 14 x + 10 x ^ { 2 } - 19 x ^ { 3 } - 18 x ^ { 4 }$$

Accepted Answer

A)  Degree: 4; leading coefficient: 19 
B)  Degree: 19; leading coefficient: $- 18$ 
C)  Degree: 3; leading coefficient: $- 19$ 
D)  Degree: 4; leading coefficient: $- 18$ 
A)  Degree: 4; leading coefficient: 19 
B)  Degree: 19; leading coefficient: $- 18$ 
C)  Degree: 3; leading coefficient: $- 19$ 
D)  Degree: 4; leading coefficient: $- 18$

Find one solution graphically and then find the remaining solutions using synthetic division. - $2 x ^ { 3 } + 5 x ^ { 2 } - 14 x - 8 = 0$

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $6 x ^ { 3 } + 16 x ^ { 2 } + 6 x - 4 = 0 ; - 1$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 \right) ; ( x + 2 )$

Provide an appropriate response. -If $y$ varies inversely as the 4 th power of $x$ and $y = 8$ when $x = - 2$ , what is $y$ when $x = 0.5$ ?

Use factoring and the root method to solve the polynomial equation. - $0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }$

Provide an appropriate response. -Which function has no vertical asymptote? Why? a. $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$ b. $f ( x ) = \frac { 2 } { x ^ { 2 } - 6 x }$ c. $f ( x ) = \frac { 3 x ^ { 2 } + 15 } { x ^ { 2 } + 6 }$ d. $f ( x ) = \frac { x + 5 } { ( x - 5 ) ( x - 3 ) }$

Determine whether the given constant is a solution to the given polynomial equation. - $7 x ^ { 3 } - 2 x ^ { 2 } + x - 6 = 0 ; 1$

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - $h ( x ) = \frac { 2 x ^ { 2 } - 8 x - 7 } { 9 x ^ { 2 } - 3 x + 8 }$

Predict the end behavior of the graph of the function. - $f ( x ) = 9 ( x - 2 ) \left( x ^ { 2 } + 2 \right)$

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Solve the polynomial equation by factoring. - $2 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $h ( x ) = \frac { ( x - 6 ) ( x + 1 ) } { x ^ { 2 } - 4 }$

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 3 } - 1 \right) \div ( x - 1 )$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 9 }$

Find the cubic or quartic function that models the data in the table. - x -2 0 1 3 y 10 15 21 33 start text left parenthesisCubicright parenthesis end text

Solve the polynomial equation by factoring. - $x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 = 0$

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 19 + 14 x + 10 x ^ { 2 } - 19 x ^ { 3 } - 18 x ^ { 4 }$

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

Find one solution graphically and then find the remaining solutions using synthetic division. - 2x3+5x2−14x−8=02 x ^ { 3 } + 5 x ^ { 2 } - 14 x - 8 = 02x3+5x2−14x−8=0

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - 6x3+16x2+6x−4=0;−16 x ^ { 3 } + 16 x ^ { 2 } + 6 x - 4 = 0 ; - 16x3+16x2+6x−4=0;−1

Determine whether the second polynomial is a factor of the first polynomial. - (9x4+19x3−2x2+x+4);(x+2)\left( 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 \right) ; ( x + 2 )(9x4+19x3−2x2+x+4);(x+2)

Provide an appropriate response. -If yyy varies inversely as the 4 th power of xxx and y=8y = 8y=8 when x=−2x = - 2x=−2 , what is yyy when x=0.5x = 0.5x=0.5 ?

Use factoring and the root method to solve the polynomial equation. - 0.1x3−9x=00.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 00.1x3−9x=0

Give the equations of any vertical asymptotes for the graphs of the rational functions. - f(x)=6x3+5x−9x2+4x−21f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }f(x)=x2+4x−216x3+5x−9​

Determine whether the given constant is a solution to the given polynomial equation. - 7x3−2x2+x−6=0;17 x ^ { 3 } - 2 x ^ { 2 } + x - 6 = 0 ; 17x3−2x2+x−6=0;1

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - h(x)=2x2−8x−79x2−3x+8h ( x ) = \frac { 2 x ^ { 2 } - 8 x - 7 } { 9 x ^ { 2 } - 3 x + 8 }h(x)=9x2−3x+82x2−8x−7​

Predict the end behavior of the graph of the function. - f(x)=9(x−2)(x2+2)f ( x ) = 9 ( x - 2 ) \left( x ^ { 2 } + 2 \right)f(x)=9(x−2)(x2+2)

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Solve the polynomial equation by factoring. - 2x3+4x2−2x−4=02 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 02x3+4x2−2x−4=0

Give the equations of any vertical asymptotes for the graphs of the rational functions. - h(x)=(x−6)(x+1)x2−4h ( x ) = \frac { ( x - 6 ) ( x + 1 ) } { x ^ { 2 } - 4 }h(x)=x2−4(x−6)(x+1)​

Use synthetic division to find the quotient and remainder. - (x3−1)÷(x−1)\left( x ^ { 3 } - 1 \right) \div ( x - 1 )(x3−1)÷(x−1)

Give the equations of any vertical asymptotes for the graphs of the rational functions. - f(x)=x−7x2−9f ( x ) = \frac { x - 7 } { x ^ { 2 } - 9 }f(x)=x2−9x−7​

Find the cubic or quartic function that models the data in the table. - x -2 0 1 3 y 10 15 21 33 start text left parenthesisCubicright parenthesis end text

Solve the polynomial equation by factoring. - x3−3x2−4x+12=0x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 = 0x3−3x2−4x+12=0

x4−18x2+32=0x ^ { 4 } - 18 x ^ { 2 } + 32 = 0x4−18x2+32=0

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x)=0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x)=0 -

State the degree and leading coefficient of the polynomial function. - f(x)=19+14x+10x2−19x3−18x4f ( x ) = 19 + 14 x + 10 x ^ { 2 } - 19 x ^ { 3 } - 18 x ^ { 4 }f(x)=19+14x+10x2−19x3−18x4

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

Find one solution graphically and then find the remaining solutions using synthetic division. - $2 x ^ { 3 } + 5 x ^ { 2 } - 14 x - 8 = 0$

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $6 x ^ { 3 } + 16 x ^ { 2 } + 6 x - 4 = 0 ; - 1$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 \right) ; ( x + 2 )$

Provide an appropriate response. -If $y$ varies inversely as the 4 th power of $x$ and $y = 8$ when $x = - 2$ , what is $y$ when $x = 0.5$ ?

Use factoring and the root method to solve the polynomial equation. - $0.1 \mathrm { x } ^ { 3 } - 9 \mathrm { x } = 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }$

Determine whether the given constant is a solution to the given polynomial equation. - $7 x ^ { 3 } - 2 x ^ { 2 } + x - 6 = 0 ; 1$

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - $h ( x ) = \frac { 2 x ^ { 2 } - 8 x - 7 } { 9 x ^ { 2 } - 3 x + 8 }$

Predict the end behavior of the graph of the function. - $f ( x ) = 9 ( x - 2 ) \left( x ^ { 2 } + 2 \right)$

Solve the polynomial equation by factoring. - $2 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 = 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $h ( x ) = \frac { ( x - 6 ) ( x + 1 ) } { x ^ { 2 } - 4 }$

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 3 } - 1 \right) \div ( x - 1 )$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 9 }$

Solve the polynomial equation by factoring. - $x ^ { 3 } - 3 x ^ { 2 } - 4 x + 12 = 0$

$x ^ { 4 } - 18 x ^ { 2 } + 32 = 0$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 19 + 14 x + 10 x ^ { 2 } - 19 x ^ { 3 } - 18 x ^ { 4 }$