Question 1

Identify the vertex of the parabola.
-$$f ( x ) = - 3 ( x - 3 ) ^ { 2 } + 8$$

Accepted Answer

A)  $( - 3,8 )$ 
B)  $( 3,8 )$ 
C)  $( 9,8 )$ 
D)  $( 3 , - 8 )$ 
A)  $( - 3,8 )$ 
B)  $( 3,8 )$ 
C)  $( 9,8 )$ 
D)  $( 3 , - 8 )$

Question 2

Solve the problem.
-$$f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$$

Accepted Answer

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

Question 3

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$$6 x ^ { 3 } + 15 x ^ { 2 } - 10 x + 3 ; x + 3$$

Accepted Answer

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

Question 4

Find all rational zeros and factor f(x).
-$$f ( x ) = 12 x ^ { 3 } + 61 x ^ { 2 } + 4 x - 5$$

Accepted Answer

A)  $- 3,4 , - 5 ; f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 5 )$ 
B)  $- \frac { 1 } { 3 } , \frac { 1 } { 4 } , - 5 ; f ( x ) = ( 3 x + 1 ) ( 4 x - 1 ) ( x + 5 )$ 
C)  $- 3,4 , - 5 ; f ( x ) = ( 3 x + 1 ) ( 4 x - 1 ) ( x + 5 )$ 
D)  $- \frac { 1 } { 12 } , 1 , - 5 ; f ( x ) = ( 12 x + 1 ) ( x - 1 ) ( x + 5 )$ 
A)  $- 3,4 , - 5 ; f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 5 )$ 
B)  $- \frac { 1 } { 3 } , \frac { 1 } { 4 } , - 5 ; f ( x ) = ( 3 x + 1 ) ( 4 x - 1 ) ( x + 5 )$ 
C)  $- 3,4 , - 5 ; f ( x ) = ( 3 x + 1 ) ( 4 x - 1 ) ( x + 5 )$ 
D)  $- \frac { 1 } { 12 } , 1 , - 5 ; f ( x ) = ( 12 x + 1 ) ( x - 1 ) ( x + 5 )$

Question 5

Find the domain and range of the function.
-$$f ( x ) = - 5 x ^ { 2 } - 80 x - 324$$

Accepted Answer

A)  Domain: $( - \infty , - 4 ] ;$ Range: $[ 0 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 8 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 4 ]$ 
D)  Domain: $( - \infty , - 4 ]$; Range: $[ 8 , \infty )$ 
A)  Domain: $( - \infty , - 4 ] ;$ Range: $[ 0 , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 8 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 4 ]$ 
D)  Domain: $( - \infty , - 4 ]$; Range: $[ 8 , \infty )$

Question 6

Solve the problem. Round your answer to two decimal places.
-The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 4 sec when the length is 64 inches, what is the period when L = 5.0625
Inches?

Accepted Answer

A)  5 sec 
B)  1.125 sec 
C)  4.5 sec 
D)  4.75 sec 
A)  5 sec 
B)  1.125 sec 
C)  4.5 sec 
D)  4.75 sec

Question 7

Given the equation or other information for a parabola, find the matching description or graph.
-$$\begin{array} { l } 
f ( x ) = a x ^ { 2 } + b x + c \
a < 0 ; b ^ { 2 } - 4 a c = 0
\end{array}$$

Accepted Answer

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

Question 8

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { x ( x - 4 ) } { x - 2 }$ 
B)  $f ( x ) = \frac { x ( x + 4 ) } { x + 2 }$ 
C)  $f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$ 
D)  $f ( x ) = \frac { x ( x + 4 ) } { ( x + 2 ) ^ { 2 } }$ 
A)  $f ( x ) = \frac { x ( x - 4 ) } { x - 2 }$ 
B)  $f ( x ) = \frac { x ( x + 4 ) } { x + 2 }$ 
C)  $f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$ 
D)  $f ( x ) = \frac { x ( x + 4 ) } { ( x + 2 ) ^ { 2 } }$

Question 9

Give the equations of any vertical asymptotes.
-$$f ( x ) = \frac { x - 8 } { x ^ { 2 } - 36 }$$

Accepted Answer

A)  $x = 6$ 
B)  $x = 8$ 
C)  $x = - 6$ 
D)  $x = 6 , x = - 6$ 
A)  $x = 6$ 
B)  $x = 8$ 
C)  $x = - 6$ 
D)  $x = 6 , x = - 6$

Question 10

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 3 ( x + 7 ) ^ { 2 } ( x - 7 ) ^ { 3 }$$

Accepted Answer

A)  4 (multiplicity 1), 7 (multiplicity 1), $- 7$ (multiplicity 1 ) 
B)  $- 7$ (multiplicity 2), 7 (multiplicity 3 ) 
C)  $- 7$ (multiplicity 3), 7 (multiplicity 2) 
D)  4 (multiplicity 1), $- 7$ (multiplicity 3), 7 (multiplicity 3) 
A)  4 (multiplicity 1), 7 (multiplicity 1), $- 7$ (multiplicity 1 ) 
B)  $- 7$ (multiplicity 2), 7 (multiplicity 3 ) 
C)  $- 7$ (multiplicity 3), 7 (multiplicity 2) 
D)  4 (multiplicity 1), $- 7$ (multiplicity 3), 7 (multiplicity 3)

Question 11

Find the correct end behavior diagram for the given polynomial function.
-$$P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 2 x + 6$$

Accepted Answer

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

Question 12

Identify the vertex of the parabola.
-$$f ( x ) = ( x - 2 ) ^ { 2 }$$

Accepted Answer

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

Question 13

Identify the vertex of the parabola.
-$$y = - 2 x ^ { 2 } - 4 x - 2$$

Accepted Answer

A)  $( 1,0 )$ 
B)  $( - 1,0 )$ 
C)  $( 0,1 )$ 
D)  $( 0 , - 1 )$ 
A)  $( 1,0 )$ 
B)  $( - 1,0 )$ 
C)  $( 0,1 )$ 
D)  $( 0 , - 1 )$

Question 14

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$$

Accepted Answer

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

Question 15

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
B)  $P ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
C)  $P ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$ 
D)  $P ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$ 
A)  $P ( x ) = - 2 x ^ { 5 } + 7 x ^ { 4 } + 9 x ^ { 3 } - 40 x ^ { 2 } + 4 x + 16$ 
B)  $P ( x ) = 2 x ^ { 6 } + 9 x ^ { 3 } - 7 x ^ { 2 } + 4 x - 16$ 
C)  $P ( x ) = x ^ { 5 } + 7 x ^ { 4 } - x ^ { 3 } - 40 x ^ { 2 } + 2 x + 16$ 
D)  $P ( x ) = - x ^ { 6 } + 7 x ^ { 5 } - x ^ { 2 } - 2 x + 16$

Question 16

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Accepted Answer

A)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } + \frac { 13 x } { 6 } + 2$ 
B)  $P ( x ) = \frac { x ^ { 3 } } { 6 } + \frac { 19 x } { 6 } - 2$ 
C)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } - \frac { 19 x } { 6 } - 2$ 
D)  $P ( x ) = \frac { x ^ { 3 } } { 6 } - \frac { 13 x } { 6 } - 2$ 
A)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } + \frac { 13 x } { 6 } + 2$ 
B)  $P ( x ) = \frac { x ^ { 3 } } { 6 } + \frac { 19 x } { 6 } - 2$ 
C)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } - \frac { 19 x } { 6 } - 2$ 
D)  $P ( x ) = \frac { x ^ { 3 } } { 6 } - \frac { 13 x } { 6 } - 2$

Question 17

Find all rational zeros and factor f(x).
-$$f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$$

Accepted Answer

A)  $1 , - 1,2 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 2 )$ 
B)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x$ 
C)  $2 , - 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 2 )$ 
D)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x$ 
A)  $1 , - 1,2 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x - 2 )$ 
B)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 ; f ( x ) = ( 2 x - 1 ) ( 2 x + 1 ) ( x$ 
C)  $2 , - 2,2 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x - 2 )$ 
D)  $\frac { 1 } { 2 } , - \frac { 1 } { 2 } , 2 ; f ( x ) = ( x - 2 ) ( x + 2 ) ( x$

Question 18

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1$ and 2

Accepted Answer

A)  $f ( 1 ) = 3$ and $f ( 2 ) = 200$ 
B)  $f ( 1 ) = - 2$ and $f ( 2 ) = 201$ 
C)  $f ( 1 ) = - 3$ and $f ( 2 ) = 200$ 
D)  $f ( 1 ) = 3$ and $f ( 2 ) = - 200$ 
A)  $f ( 1 ) = 3$ and $f ( 2 ) = 200$ 
B)  $f ( 1 ) = - 2$ and $f ( 2 ) = 201$ 
C)  $f ( 1 ) = - 3$ and $f ( 2 ) = 200$ 
D)  $f ( 1 ) = 3$ and $f ( 2 ) = - 200$

Question 19

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$$

Accepted Answer

A)  $i , - i , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$ 
B)  $i , - i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $i , - i , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
D)  $i , - i , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$ 
A)  $i , - i , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$ 
B)  $i , - i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $i , - i , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
D)  $i , - i , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$

Question 20

Solve the problem.
-The graph of $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$ is shown below. Use the graph to factor $f ( x )$.

Accepted Answer

A)  $f ( x ) = - ( x + 4 ) ( x + 1 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 4 ) ( x + 1 ) ( x - 1 )$ 
C)  $f ( x ) = ( x - 4 ) ( x + 1 ) ( x + 4 )$ 
D)  $f ( x ) = ( x - 4 ) ( x + 1 ) ( x - 1 )$ 
A)  $f ( x ) = - ( x + 4 ) ( x + 1 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 4 ) ( x + 1 ) ( x - 1 )$ 
C)  $f ( x ) = ( x - 4 ) ( x + 1 ) ( x + 4 )$ 
D)  $f ( x ) = ( x - 4 ) ( x + 1 ) ( x - 1 )$

Identify the vertex of the parabola. - $f ( x ) = - 3 ( x - 3 ) ^ { 2 } + 8$

Solve the problem. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$ $Solve the problem. - f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 3 } + 15 x ^ { 2 } - 10 x + 3 ; x + 3$

Find all rational zeros and factor f(x). - $f ( x ) = 12 x ^ { 3 } + 61 x ^ { 2 } + 4 x - 5$

Find the domain and range of the function. - $f ( x ) = - 5 x ^ { 2 } - 80 x - 324$

Solve the problem. Round your answer to two decimal places. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 4 sec when the length is 64 inches, what is the period when L = 5.0625 Inches?

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac=0

Find an equation for the rational function graph. -

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 8 } { x ^ { 2 } - 36 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 3 ( x + 7 ) ^ { 2 } ( x - 7 ) ^ { 3 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 2 x + 6$

Identify the vertex of the parabola. - $f ( x ) = ( x - 2 ) ^ { 2 }$

Identify the vertex of the parabola. - $y = - 2 x ^ { 2 } - 4 x - 2$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$

Find the equation that the given graph represents. -

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Find all rational zeros and factor f(x). - $f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1$ and 2

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

Solve the problem. -The graph of $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4 is shown below. Use the graph to factor f ( x ) .$

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Identify the vertex of the parabola. - f(x)=−3(x−3)2+8f ( x ) = - 3 ( x - 3 ) ^ { 2 } + 8f(x)=−3(x−3)2+8

Solve the problem. - f(x)=−13x2f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }f(x)=−31​x2

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 6x3+15x2−10x+3;x+36 x ^ { 3 } + 15 x ^ { 2 } - 10 x + 3 ; x + 36x3+15x2−10x+3;x+3

Find all rational zeros and factor f(x). - f(x)=12x3+61x2+4x−5f ( x ) = 12 x ^ { 3 } + 61 x ^ { 2 } + 4 x - 5f(x)=12x3+61x2+4x−5

Find the domain and range of the function. - f(x)=−5x2−80x−324f ( x ) = - 5 x ^ { 2 } - 80 x - 324f(x)=−5x2−80x−324

Solve the problem. Round your answer to two decimal places. -The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 4 sec when the length is 64 inches, what is the period when L = 5.0625 Inches?

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac=0

Find an equation for the rational function graph. -

Give the equations of any vertical asymptotes. - f(x)=x−8x2−36f ( x ) = \frac { x - 8 } { x ^ { 2 } - 36 }f(x)=x2−36x−8​

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=3(x+7)2(x−7)3f ( x ) = 3 ( x + 7 ) ^ { 2 } ( x - 7 ) ^ { 3 }f(x)=3(x+7)2(x−7)3

Find the correct end behavior diagram for the given polynomial function. - P(x)=2x3+9x2−2x+6P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 2 x + 6P(x)=2x3+9x2−2x+6

Identify the vertex of the parabola. - f(x)=(x−2)2f ( x ) = ( x - 2 ) ^ { 2 }f(x)=(x−2)2

Identify the vertex of the parabola. - y=−2x2−4x−2y = - 2 x ^ { 2 } - 4 x - 2y=−2x2−4x−2

Sketch the graph of the rational function. - f(x)=x2−x−12x+4f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }f(x)=x+4x2−x−12​

Find the equation that the given graph represents. -

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −3,−1,4- 3 , - 1,4−3,−1,4 and P(2)=5P ( 2 ) = 5P(2)=5

Find all rational zeros and factor f(x). - f(x)=4x3−8x2−x+2f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2f(x)=4x3−8x2−x+2

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=8x5−9x3+6x2−8;1f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1f(x)=8x5−9x3+6x2−8;1 and 2

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−10x3+23x2−10x+22f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22f(x)=x4−10x3+23x2−10x+22

Solve the problem. -The graph of f(x)=x3+4x2−x−4f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4f(x)=x3+4x2−x−4 is shown below. Use the graph to factor f(x)f ( x )f(x) .

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Identify the vertex of the parabola. - $f ( x ) = - 3 ( x - 3 ) ^ { 2 } + 8$

Solve the problem. - $f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$ $Solve the problem. - f ( x ) = - \frac { 1 } { 3 } x ^ { 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $6 x ^ { 3 } + 15 x ^ { 2 } - 10 x + 3 ; x + 3$

Find all rational zeros and factor f(x). - $f ( x ) = 12 x ^ { 3 } + 61 x ^ { 2 } + 4 x - 5$

Find the domain and range of the function. - $f ( x ) = - 5 x ^ { 2 } - 80 x - 324$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 8 } { x ^ { 2 } - 36 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 3 ( x + 7 ) ^ { 2 } ( x - 7 ) ^ { 3 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 2 x ^ { 3 } + 9 x ^ { 2 } - 2 x + 6$

Identify the vertex of the parabola. - $f ( x ) = ( x - 2 ) ^ { 2 }$

Identify the vertex of the parabola. - $y = - 2 x ^ { 2 } - 4 x - 2$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Find all rational zeros and factor f(x). - $f ( x ) = 4 x ^ { 3 } - 8 x ^ { 2 } - x + 2$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 8 x ^ { 5 } - 9 x ^ { 3 } + 6 x ^ { 2 } - 8 ; 1$ and 2

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

Solve the problem. -The graph of $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x - 4 is shown below. Use the graph to factor f ( x ) .$