Question 1

Subtract.
-$$\left( 6 x ^ { 3 } + 2 x y ^ { 2 } + 8 y ^ { 3 } \right) - \left( 4 x ^ { 3 } + 12 x ^ { 2 } y + 9 x y ^ { 2 } + 5 y ^ { 3 } \right)$$

Accepted Answer

A)  $- 2 x ^ { 3 } + 12 x ^ { 2 } y + 7 x y ^ { 2 } - 3 y ^ { 3 }$ 
B)  $2 x ^ { 3 } + 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$ 
C)  $10 x ^ { 3 } + 12 x ^ { 2 } y + 15 x y ^ { 2 } + 13 y ^ { 3 }$ 
D)  $2 x ^ { 3 } - 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$ 
A)  $- 2 x ^ { 3 } + 12 x ^ { 2 } y + 7 x y ^ { 2 } - 3 y ^ { 3 }$ 
B)  $2 x ^ { 3 } + 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$ 
C)  $10 x ^ { 3 } + 12 x ^ { 2 } y + 15 x y ^ { 2 } + 13 y ^ { 3 }$ 
D)  $2 x ^ { 3 } - 12 x ^ { 2 } y - 7 x y ^ { 2 } + 3 y ^ { 3 }$

Question 2

Match the polynomial function with its graph.
-$$f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )$$

Accepted Answer

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

Question 3

Solve.
-A certain rectangle's length is $3 \mathrm { ft }$ longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Accepted Answer

A)  $11 \mathrm { ft }$ by $16 \mathrm { ft }$ 
B)  $11 \mathrm { ft }$ by $14 \mathrm { ft }$ 
C)  $13 \mathrm { ft }$ by $16 \mathrm { ft }$ 
D)  $12 \mathrm { ft }$ by $15 \mathrm { ft }$ 
A)  $11 \mathrm { ft }$ by $16 \mathrm { ft }$ 
B)  $11 \mathrm { ft }$ by $14 \mathrm { ft }$ 
C)  $13 \mathrm { ft }$ by $16 \mathrm { ft }$ 
D)  $12 \mathrm { ft }$ by $15 \mathrm { ft }$

Question 4

Factor.
-$$\frac { 1 } { 4 } - 49 z ^ { 2 }$$

Accepted Answer

A)  $\left( \frac { 1 } { 2 } + 7 z \right) ^ { 2 }$ 
B)  $\left( \frac { 1 } { 2 } + 7 \mathrm { z } \right) \left( \frac { 1 } { 2 } - 7 \mathrm { z } \right)$ 
C)  $\left( \frac { 1 } { 2 } - 7 \mathrm { z } \right) ^ { 2 }$ 
D)  prime polynomial 
A)  $\left( \frac { 1 } { 2 } + 7 z \right) ^ { 2 }$ 
B)  $\left( \frac { 1 } { 2 } + 7 \mathrm { z } \right) \left( \frac { 1 } { 2 } - 7 \mathrm { z } \right)$ 
C)  $\left( \frac { 1 } { 2 } - 7 \mathrm { z } \right) ^ { 2 }$ 
D)  prime polynomial

Question 5

Divide.
-$$\frac { - 20 x ^ { 5 } y ^ { 7 } + 8 x ^ { 4 } y ^ { 5 } + 3 x ^ { 3 } y ^ { 4 } } { 4 x ^ { 3 } y ^ { 4 } }$$

Accepted Answer

A)  $- 5 x ^ { 2 } y ^ { 7 } + 2 x ^ { 3 } y ^ { 4 } + \frac { 3 } { 4 }$ 
B)  $- 5 x ^ { 2 } y ^ { 3 } + 2 x y ^ { 5 } + \frac { 3 } { 4 }$ 
C)  $- 20 x ^ { 2 } y ^ { 3 } + 8 x y + 3$ 
D)  $- 5 x ^ { 2 } y ^ { 3 } + 2 x y + \frac { 3 } { 4 }$ 
A)  $- 5 x ^ { 2 } y ^ { 7 } + 2 x ^ { 3 } y ^ { 4 } + \frac { 3 } { 4 }$ 
B)  $- 5 x ^ { 2 } y ^ { 3 } + 2 x y ^ { 5 } + \frac { 3 } { 4 }$ 
C)  $- 20 x ^ { 2 } y ^ { 3 } + 8 x y + 3$ 
D)  $- 5 x ^ { 2 } y ^ { 3 } + 2 x y + \frac { 3 } { 4 }$

Question 6

Factor.
-$$x ^ { 3 } - 27$$

Accepted Answer

A)  $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$ 
B)  $( x + 27 ) ( x + 1 ) ( x - 1 )$ 
C)  $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$ 
D)  $( x - 3 ) \left( x ^ { 2 } + 9 \right)$ 
A)  $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$ 
B)  $( x + 27 ) ( x + 1 ) ( x - 1 )$ 
C)  $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$ 
D)  $( x - 3 ) \left( x ^ { 2 } + 9 \right)$

Question 7

Factor the polynomial.
-$$x ^ { 3 } + 6 x + x ^ { 2 } + 6$$

Accepted Answer

A)  $\left( x ^ { 2 } + 1 \right) ( 6 x + 1 )$ 
B)  $( 6 x + 1 ) ( x + 1 )$ 
C)  $\left( x ^ { 2 } + 6 \right) ( x + 1 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x + 6 )$ 
A)  $\left( x ^ { 2 } + 1 \right) ( 6 x + 1 )$ 
B)  $( 6 x + 1 ) ( x + 1 )$ 
C)  $\left( x ^ { 2 } + 6 \right) ( x + 1 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x + 6 )$

Question 8

For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$$
-$$f ( x ) = - 2 x ^ { 4 } + 12 x ^ { 3 } + 13 x ^ { 2 } + 15 x - 56 ; g ( x ) = x - 7$$

Accepted Answer

A)  $- 2 x ^ { 3 } - 2 x ^ { 2 } + x - 8 ; x \neq - 7$ 
B)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x - 8 ; x \neq 7$ 
C)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x - 8 + \frac { 112 } { 7 - x } ; x \neq - 7$ 
D)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x + 8 ; x \neq 7$ 
A)  $- 2 x ^ { 3 } - 2 x ^ { 2 } + x - 8 ; x \neq - 7$ 
B)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x - 8 ; x \neq 7$ 
C)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x - 8 + \frac { 112 } { 7 - x } ; x \neq - 7$ 
D)  $- 2 x ^ { 3 } - 2 x ^ { 2 } - x + 8 ; x \neq 7$

Question 9

Solve.
-Find the volume of the box.

Accepted Answer

A)  $\left( 9 x ^ { 3 } - 57 x ^ { 2 } + 88 x \right)$ cu units 
B)  $\left( 9 x ^ { 2 } - 57 x + 89 \right)$ cu units 
C)  $\left( - 9 x ^ { 2 } + 39 x + 89 \right)$ cu units 
D)  $\left( - 9 x ^ { 3 } + 39 x ^ { 2 } + 88 x \right)$ cu units 
A)  $\left( 9 x ^ { 3 } - 57 x ^ { 2 } + 88 x \right)$ cu units 
B)  $\left( 9 x ^ { 2 } - 57 x + 89 \right)$ cu units 
C)  $\left( - 9 x ^ { 2 } + 39 x + 89 \right)$ cu units 
D)  $\left( - 9 x ^ { 3 } + 39 x ^ { 2 } + 88 x \right)$ cu units

Question 10

Factor out the greatest common factor.
-$18 x ^ { 3 } - 6 x ^ { 2 } + 10 x$

Accepted Answer

A)  $2 \left( 9 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
B)  $2 x \left( 9 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
C)  $x \left( 18 x ^ { 2 } - 6 x + 10 \right)$ 
D)  $2 x \left( 9 x ^ { 2 } - 3 x + 5 \right)$ 
A)  $2 \left( 9 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
B)  $2 x \left( 9 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
C)  $x \left( 18 x ^ { 2 } - 6 x + 10 \right)$ 
D)  $2 x \left( 9 x ^ { 2 } - 3 x + 5 \right)$

Question 11

Factor. Assume that variables used as exponents represent positive integers.
-$9 x ^ { 2 n } - 4$

Accepted Answer

A)  $\left( 3 x ^ { n } - 2 \right) ^ { 2 }$ 
B)  $\left( 3 x ^ { n } + 2 \right) ^ { 2 }$ 
C)  $\left( 3 x ^ { n } + 2 \right) \left( 3 x ^ { n } - 2 \right)$ 
D)  prime polynomial 
A)  $\left( 3 x ^ { n } - 2 \right) ^ { 2 }$ 
B)  $\left( 3 x ^ { n } + 2 \right) ^ { 2 }$ 
C)  $\left( 3 x ^ { n } + 2 \right) \left( 3 x ^ { n } - 2 \right)$ 
D)  prime polynomial

Question 12

Factor.
-$( 5 x + y ) ^ { 2 } - 36$

Accepted Answer

A)  $( 5 x + y - 6 ) ^ { 2 }$ 
B)  $( 5 x + y + 6 ) ( 5 x + y - 6 )$ 
C)  $( 5 x + y + 6 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $( 5 x + y - 6 ) ^ { 2 }$ 
B)  $( 5 x + y + 6 ) ( 5 x + y - 6 )$ 
C)  $( 5 x + y + 6 ) ^ { 2 }$ 
D)  prime polynomial

Question 13

Factor.
-$x ^ { 3 } + 8$

Accepted Answer

A)  $( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
B)  $( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
C)  $( x - 8 ) ( x + 1 ) ( x - 1 )$ 
D)  $( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$ 
A)  $( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
B)  $( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right)$ 
C)  $( x - 8 ) ( x + 1 ) ( x - 1 )$ 
D)  $( x - 2 ) \left( x ^ { 2 } + 2 x + 4 \right)$

Question 14

Perform the indicated operation.
-$$\left( x ^ { 3 } y ^ { 3 } z + 20 x y z ^ { 5 } + 11 x ^ { 4 } y ^ { 6 } \right) \div \left( 4 x y z ^ { 5 } \right)$$

Accepted Answer

A)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } + 5 + \frac { 11 x ^ { 3 } y ^ { 6 } } { 4 z ^ { 5 } }$ 
B)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } + 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$ 
C)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 5 } } - 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$ 
D)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } - 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$ 
A)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } + 5 + \frac { 11 x ^ { 3 } y ^ { 6 } } { 4 z ^ { 5 } }$ 
B)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } + 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$ 
C)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 5 } } - 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$ 
D)  $\frac { x ^ { 2 } y ^ { 2 } } { 4 z ^ { 4 } } - 5 + \frac { 11 x ^ { 3 } y ^ { 5 } } { 4 z ^ { 5 } }$

Question 15

Solve.
-The total cost (in dollars) for a certain company to produce $x$ glass jars per week is given by the polynomial function $\mathrm { C } ( \mathrm { x } ) = 0.4 \mathrm { x } + 40,000$. Find the total cost of producing 80,000 jars per week.

Accepted Answer

A)  $\$ 80,040$ 
B)  $\$ 72,000$ 
C)  $\$ 32,000$ 
D)  $\$ 40.40$ 
A)  $\$ 80,040$ 
B)  $\$ 72,000$ 
C)  $\$ 32,000$ 
D)  $\$ 40.40$

Question 16

Multiply.
-$$[ ( 4 x - 4 ) + 7 y ] [ ( 4 x - 4 ) - 7 y ]$$

Accepted Answer

A)  $16 x ^ { 2 } - 32 x + 16 + 49 y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 32 x + 16 - 49 y ^ { 2 }$ 
C)  $16 x ^ { 2 } - 32 x + 16 - 49 y ^ { 2 }$ 
D)  $16 x ^ { 2 } - 32 x + 16 + 56 x y - 56 y + 49 y ^ { 2 }$ 
A)  $16 x ^ { 2 } - 32 x + 16 + 49 y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 32 x + 16 - 49 y ^ { 2 }$ 
C)  $16 x ^ { 2 } - 32 x + 16 - 49 y ^ { 2 }$ 
D)  $16 x ^ { 2 } - 32 x + 16 + 56 x y - 56 y + 49 y ^ { 2 }$

Question 17

Solve the equation.
-$$y ^ { 2 } + 3 y = 108$$

Accepted Answer

A)  $\{ 12 , - 9 \}$ 
B)  $\{ - 12,9 \}$ 
C)  $\{ 12,9 \}$ 
D)  $\{ - 12,1 \}$ 
A)  $\{ 12 , - 9 \}$ 
B)  $\{ - 12,9 \}$ 
C)  $\{ 12,9 \}$ 
D)  $\{ - 12,1 \}$

Question 18

Multiply.
-$12 a b ^ { 2 } \left( 11 a ^ { 2 } b ^ { 3 } + 3 a b \right)$

Accepted Answer

A)  $132 a ^ { 2 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$ 
B)  $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$ 
C)  $132 a ^ { 3 } b ^ { 4 } + 36 a ^ { 2 } b ^ { 3 }$ 
D)  $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 2 }$ 
A)  $132 a ^ { 2 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$ 
B)  $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 3 }$ 
C)  $132 a ^ { 3 } b ^ { 4 } + 36 a ^ { 2 } b ^ { 3 }$ 
D)  $132 a ^ { 3 } b ^ { 5 } + 36 a ^ { 2 } b ^ { 2 }$

Question 19

Match the polynomial function with its graph.
-$$f ( x ) = 2 x ^ { 2 } - 9 x + 10$$

Accepted Answer

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

Question 20

Multiply.
-$$( 4 y + 11 ) \left( 7 y ^ { 2 } - 2 y - 9 \right)$$

Accepted Answer

A)  $28 y ^ { 3 } - 8 y ^ { 2 } - 36 y + 11$ 
B)  $28 y ^ { 3 } + 69 y ^ { 2 } - 58 y - 99$ 
C)  $28 y ^ { 3 } + 85 y ^ { 2 } + 58 y + 99$ 
D)  $105 y ^ { 2 } - 30 y - 135$ 
A)  $28 y ^ { 3 } - 8 y ^ { 2 } - 36 y + 11$ 
B)  $28 y ^ { 3 } + 69 y ^ { 2 } - 58 y - 99$ 
C)  $28 y ^ { 3 } + 85 y ^ { 2 } + 58 y + 99$ 
D)  $105 y ^ { 2 } - 30 y - 135$

Subtract. - $\left( 6 x ^ { 3 } + 2 x y ^ { 2 } + 8 y ^ { 3 } \right) - \left( 4 x ^ { 3 } + 12 x ^ { 2 } y + 9 x y ^ { 2 } + 5 y ^ { 3 } \right)$

Match the polynomial function with its graph. - $f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )$

Solve. -A certain rectangle's length is $3 \mathrm { ft }$ longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Factor. - $\frac { 1 } { 4 } - 49 z ^ { 2 }$

Divide. - $\frac { - 20 x ^ { 5 } y ^ { 7 } + 8 x ^ { 4 } y ^ { 5 } + 3 x ^ { 3 } y ^ { 4 } } { 4 x ^ { 3 } y ^ { 4 } }$

Factor. - $x ^ { 3 } - 27$

Factor the polynomial. - $x ^ { 3 } + 6 x + x ^ { 2 } + 6$

For the given f(x $f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$ - $f ( x ) = - 2 x ^ { 4 } + 12 x ^ { 3 } + 13 x ^ { 2 } + 15 x - 56 ; g ( x ) = x - 7$

Solve. -Find the volume of the box.

Factor out the greatest common factor. - $18 x ^ { 3 } - 6 x ^ { 2 } + 10 x$

Factor. Assume that variables used as exponents represent positive integers. - $9 x ^ { 2 n } - 4$

Factor. - $( 5 x + y ) ^ { 2 } - 36$

Factor. - $x ^ { 3 } + 8$

Perform the indicated operation. - $\left( x ^ { 3 } y ^ { 3 } z + 20 x y z ^ { 5 } + 11 x ^ { 4 } y ^ { 6 } \right) \div \left( 4 x y z ^ { 5 } \right)$

Solve. -The total cost (in dollars) for a certain company to produce $x$ glass jars per week is given by the polynomial function $\mathrm { C } ( \mathrm { x } ) = 0.4 \mathrm { x } + 40,000$ . Find the total cost of producing 80,000 jars per week.

Multiply. - $[ ( 4 x - 4 ) + 7 y ] [ ( 4 x - 4 ) - 7 y ]$

Solve the equation. - $y ^ { 2 } + 3 y = 108$

Multiply. - $12 a b ^ { 2 } \left( 11 a ^ { 2 } b ^ { 3 } + 3 a b \right)$

Match the polynomial function with its graph. - $f ( x ) = 2 x ^ { 2 } - 9 x + 10$

Multiply. - $( 4 y + 11 ) \left( 7 y ^ { 2 } - 2 y - 9 \right)$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 5: Polynomials and Polynomial Functions

Subtract. - (6x3+2xy2+8y3)−(4x3+12x2y+9xy2+5y3)\left( 6 x ^ { 3 } + 2 x y ^ { 2 } + 8 y ^ { 3 } \right) - \left( 4 x ^ { 3 } + 12 x ^ { 2 } y + 9 x y ^ { 2 } + 5 y ^ { 3 } \right)(6x3+2xy2+8y3)−(4x3+12x2y+9xy2+5y3)

Match the polynomial function with its graph. - f(x)=(x−4)(x−3)(x−1)f ( x ) = ( x - 4 ) ( x - 3 ) ( x - 1 )f(x)=(x−4)(x−3)(x−1)

Solve. -A certain rectangle's length is 3ft3 \mathrm { ft }3ft longer than its width. If the area of the rectangle is 180 square feet, find its dimensions.

Factor. - 14−49z2\frac { 1 } { 4 } - 49 z ^ { 2 }41​−49z2

Divide. - −20x5y7+8x4y5+3x3y44x3y4\frac { - 20 x ^ { 5 } y ^ { 7 } + 8 x ^ { 4 } y ^ { 5 } + 3 x ^ { 3 } y ^ { 4 } } { 4 x ^ { 3 } y ^ { 4 } }4x3y4−20x5y7+8x4y5+3x3y4​

Factor. - x3−27x ^ { 3 } - 27x3−27

Factor the polynomial. - x3+6x+x2+6x ^ { 3 } + 6 x + x ^ { 2 } + 6x3+6x+x2+6