Question 1

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-$$f ( x ) = x ^ { 2 } - 5 x - 55$$

Accepted Answer

A)  5,13 
B)  $- 5,11$ 
C)  $4 , - 10$ 
D)  $6 , - 11$ 
A)  5,13 
B)  $- 5,11$ 
C)  $4 , - 10$ 
D)  $6 , - 11$

Question 2

Choose the polynomial that has the given factor.
-x - 5

Accepted Answer

A)  $x ^ { 2 } + 4 x - 45$ 
B)  $x ^ { 2 } - 14 x + 45$ 
C)  $x ^ { 2 } + 4 x + 45$ 
D)  $x ^ { 2 } + 14 x + 45$ 
A)  $x ^ { 2 } + 4 x - 45$ 
B)  $x ^ { 2 } - 14 x + 45$ 
C)  $x ^ { 2 } + 4 x + 45$ 
D)  $x ^ { 2 } + 14 x + 45$

Question 3

Choose the polynomial that has the given factor.
-$5 x - 4$

Accepted Answer

A)  $x ^ { 2 } - 48 x + 32$ 
B)  $10 x ^ { 2 } + 32 x + 32$ 
C)  $10 x ^ { 2 } - 48 x - 32$ 
D)  $10 x ^ { 2 } - 48 x + 32$ 
A)  $x ^ { 2 } - 48 x + 32$ 
B)  $10 x ^ { 2 } + 32 x + 32$ 
C)  $10 x ^ { 2 } - 48 x - 32$ 
D)  $10 x ^ { 2 } - 48 x + 32$

Question 4

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 6 x y + 9 y ^ { 2 }$$

Accepted Answer

A)  $( x + 3 y ) ^ { 2 }$ 
B)  Prime 
C)  $( x - 3 y ) ^ { 2 }$ 
D)  $( x + 3 y ) ( x - 3 y )$ 
A)  $( x + 3 y ) ^ { 2 }$ 
B)  Prime 
C)  $( x - 3 y ) ^ { 2 }$ 
D)  $( x + 3 y ) ( x - 3 y )$

Question 5

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The length of a room is 8 feet more than the width. The room has a floor area of 425 square feet. Find the dimensions of the room.

Accepted Answer

A)  Length: 33 feet; Width: 25 feet 
B)  Length: 28 feet; Width: 20 feet 
C)  Length: 17 feet; Width: 9 feet 
D)  Length: 25 feet; Width: 17 feet 
A)  Length: 33 feet; Width: 25 feet 
B)  Length: 28 feet; Width: 20 feet 
C)  Length: 17 feet; Width: 9 feet 
D)  Length: 25 feet; Width: 17 feet

Question 6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$- x ^ { 2 } - 5 x + 24$$

Accepted Answer

A)  $- ( x - 3 ) ( x + 8 )$ 
B)  $- ( x - 3 ) ( x - 8 )$ 
C)  $( x + 3 ) ( x - 8 )$ 
D)  Prime 
A)  $- ( x - 3 ) ( x + 8 )$ 
B)  $- ( x - 3 ) ( x - 8 )$ 
C)  $( x + 3 ) ( x - 8 )$ 
D)  Prime

Question 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - 14 x + 48$$

Accepted Answer

A)  $( x - 24 ) ( x - 2 )$ 
B)  $( x - 6 ) ( x - 8 )$ 
C)  $( x + 6 ) ( x + 8 )$ 
D)  Prime 
A)  $( x - 24 ) ( x - 2 )$ 
B)  $( x - 6 ) ( x - 8 )$ 
C)  $( x + 6 ) ( x + 8 )$ 
D)  Prime

Question 8

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The height, in feet, of a free-falling object t seconds after being dropped from an initial height s can be found using the function $h ( t ) = - 16 t ^ { 2 } + s$

Accepted Answer

A)  14.5 seconds 
B)  15 seconds 
C)  13 seconds 
D)  12 seconds 
A)  14.5 seconds 
B)  15 seconds 
C)  13 seconds 
D)  12 seconds

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - x - 54$$

Accepted Answer

A)  $( x - 54 ) ( x + 1 )$ 
B)  $( x + 6 ) ( x - 9 )$ 
C)  $( x - 6 ) ( x + 9 )$ 
D)  Prime 
A)  $( x - 54 ) ( x + 1 )$ 
B)  $( x + 6 ) ( x - 9 )$ 
C)  $( x - 6 ) ( x + 9 )$ 
D)  Prime

Question 10

Find the GCF.
-30,40,70

Accepted Answer

A)  20 
B)  2 
C)  10 
D)  5 
A)  20 
B)  2 
C)  10 
D)  5

Question 11

Factor the GCF out of the given expression.
-9x + 27

Accepted Answer

A)  3(x + 9) 
B)  9 
C)  9(x + 27) 
D)  9(x + 3) 
A)  3(x + 9) 
B)  9 
C)  9(x + 27) 
D)  9(x + 3)

Question 12

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$p ^ { 6 } + q ^ { 24 } r ^ { 18 }$$

Accepted Answer

A)  $\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)$ 
B)  $\left( \mathrm { p } ^ { 3 } + \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right) \left( \mathrm { p } ^ { 3 } - \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right)$ 
C)  $\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 2 } + p q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 2 } - q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right)$ 
D)  $\left( p ^ { 2 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)$ 
A)  $\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)$ 
B)  $\left( \mathrm { p } ^ { 3 } + \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right) \left( \mathrm { p } ^ { 3 } - \mathrm { q } ^ { 12 } \mathrm { r } ^ { 9 } \right)$ 
C)  $\left( p + q ^ { 4 } r ^ { 3 } \right) \left( p - q ^ { 4 } r ^ { 3 } \right) \left( p ^ { 2 } + p q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 2 } - q ^ { 4 } r ^ { 3 } + q ^ { 8 } r ^ { 6 } \right)$ 
D)  $\left( p ^ { 2 } + q ^ { 8 } r ^ { 6 } \right) \left( p ^ { 4 } - p ^ { 2 } q ^ { 8 } r ^ { 6 } + q ^ { 16 } r ^ { 12 } \right)$

Question 13

Solve the problem.
-Let $f ( x ) = - x ^ { 2 } + 4 x$. Find all values $x$ for which $f ( x ) = - 21$.

Accepted Answer

A)  4,0 
B)  $7 , - 3$ 
C)  $- 7,3$ 
D)  $\frac { 4 } { 21 } , \frac { 1 } { - 21 }$ 
A)  4,0 
B)  $7 , - 3$ 
C)  $- 7,3$ 
D)  $\frac { 4 } { 21 } , \frac { 1 } { - 21 }$

Question 14

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } - 2 x + 1$$

Accepted Answer

A)  $( x + 1 ) ( x - 1 )$ 
B)  $( x + 1 ) ^ { 2 }$ 
C)  $( x + 2 ) ( x - 2 )$ 
D)  $( x - 1 ) ^ { 2 }$ 
A)  $( x + 1 ) ( x - 1 )$ 
B)  $( x + 1 ) ^ { 2 }$ 
C)  $( x + 2 ) ( x - 2 )$ 
D)  $( x - 1 ) ^ { 2 }$

Question 15

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$16 x ^ { 4 } + 56 x ^ { 3 } - 32 x ^ { 2 }$

Accepted Answer

A)  $8 x ( 2 x + 1 ) ( x - 4 )$ 
B)  $8 x ^ { 2 } ( 2 x - 1 ) ( x + 4 )$ 
C)  $x ^ { 2 } ( 2 x - 1 ) ( 8 x + 32 )$ 
D)  $\left( 16 x ^ { 2 } - 8 \right) \left( x ^ { 2 } + 4 \right)$ 
A)  $8 x ( 2 x + 1 ) ( x - 4 )$ 
B)  $8 x ^ { 2 } ( 2 x - 1 ) ( x + 4 )$ 
C)  $x ^ { 2 } ( 2 x - 1 ) ( 8 x + 32 )$ 
D)  $\left( 16 x ^ { 2 } - 8 \right) \left( x ^ { 2 } + 4 \right)$

Question 16

Factor the GCF out of the given expression.
-$16 w x - 16 w y - 20 w z$

Accepted Answer

A)  $16 w ( x - 16 y - 20 z )$ 
B)  $4 w ( 4 x - 4 y - 5 z )$ 
C)  $4 ( 4 w x - 4 w y - 5 w z )$ 
D)  $4 w ( 4 x - 16 w y - 20 w z )$ 
A)  $16 w ( x - 16 y - 20 z )$ 
B)  $4 w ( 4 x - 4 y - 5 z )$ 
C)  $4 ( 4 w x - 4 w y - 5 w z )$ 
D)  $4 w ( 4 x - 16 w y - 20 w z )$

Question 17

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-$$f ( x ) = x ^ { 2 } - 6 x + 10$$

Accepted Answer

A)  5,2 
B)  4,1 
C)  $- 7 , - 7$ 
D)  $5 , - 2$ 
A)  5,2 
B)  4,1 
C)  $- 7 , - 7$ 
D)  $5 , - 2$

Question 18

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The length of a rectangular frame is 6 centimeters more than the width. The area inside the frame is 72 square centimeters. Find the width of the frame.

Accepted Answer

A)  18 centimeters 
B)  12 centimeters 
C)  8 centimeters 
D)  6 centimeters 
A)  18 centimeters 
B)  12 centimeters 
C)  8 centimeters 
D)  6 centimeters

Question 19

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$3 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }$

Accepted Answer

A)  $3 x ( x - 3 y ) ( x + 5 y )$ 
B)  $\left( 3 x ^ { 2 } + 9 x y \right) ( x - 5 y )$ 
C)  $( x - 3 y ) \left( 3 x ^ { 2 } + 15 x y \right)$ 
D)  $3 x ( x + 3 y ) ( x - 5 y )$ 
A)  $3 x ( x - 3 y ) ( x + 5 y )$ 
B)  $\left( 3 x ^ { 2 } + 9 x y \right) ( x - 5 y )$ 
C)  $( x - 3 y ) \left( 3 x ^ { 2 } + 15 x y \right)$ 
D)  $3 x ( x + 3 y ) ( x - 5 y )$

Question 20

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-The product of the page numbers on two facing pages of a book is 506. Find the page numbers.

Accepted Answer

A)  21   23 
B)  21   22 
C)  22   23 
D)  22   24 
A)  21   23 
B)  21   22 
C)  22   23 
D)  22   24

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. - $f ( x ) = x ^ { 2 } - 5 x - 55$

Choose the polynomial that has the given factor. -x - 5

Choose the polynomial that has the given factor. - $5 x - 4$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 6 x y + 9 y ^ { 2 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The length of a room is 8 feet more than the width. The room has a floor area of 425 square feet. Find the dimensions of the room.

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $- x ^ { 2 } - 5 x + 24$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 14 x + 48$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The height, in feet, of a free-falling object t seconds after being dropped from an initial height s can be found using the function $h ( t ) = - 16 t ^ { 2 } + s$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - x - 54$

Find the GCF. -30,40,70

Factor the GCF out of the given expression. -9x + 27

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $p ^ { 6 } + q ^ { 24 } r ^ { 18 }$

Solve the problem. -Let $f ( x ) = - x ^ { 2 } + 4 x$ . Find all values $x$ for which $f ( x ) = - 21$ .

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } - 2 x + 1$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $16 x ^ { 4 } + 56 x ^ { 3 } - 32 x ^ { 2 }$

Factor the GCF out of the given expression. - $16 w x - 16 w y - 20 w z$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. - $f ( x ) = x ^ { 2 } - 6 x + 10$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The length of a rectangular frame is 6 centimeters more than the width. The area inside the frame is 72 square centimeters. Find the width of the frame.

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -The product of the page numbers on two facing pages of a book is 506. Find the page numbers.

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring and Quadratic Equations

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. - f(x)=x2−5x−55f ( x ) = x ^ { 2 } - 5 x - 55f(x)=x2−5x−55